This is mostly based on my memories from living there, for about a year, in 2010 and 2011. I didn't visit since then, even though I'd really love to. Things in Greece are not looking well recently, and I'll probably be happier keeping only the nice memories.
Patra is a sister-city of my birthplace, Bydgoszcz.
Save yourself the bother. Take the bus, the ferry, the bike, but just give up on hitch hiking.
(If you wonder why is it such a problem, let me explain, as the situation is similar in other parts of Greece, and the same logic applies: illegal immigrants. Drivers won't stop where the immigrants tend to stick around - out of fear. And they are right. Stay alert.)
Water is life, but in my life I've never before lived in a place without a river, or a lake, or some other sort of a sweet water pond. Patra's tiny rivers exist only in the winter, which is rainy and not snowy, because δεν κάνει κρύο στην Ελλάδα.
So - there is the sea! The beach, like in most of Greece, is rocky and not sandy, but it's fine - the sand doesn't stick to your feet, and you get used to it quickly if you go there often. And since it's never cold in Greece, (the coldest day of that winter was around 3'C), you can practically swim in the sea all year long. Yay!
It was late September, Poland was already below freezing at night, and it was my first night ever in the south of Europe. Impossible to sleep. Too hot.
Next day, I've noticed the locals wear sweaters. What?
You can gradually adjust to the heat. The best way, as a person from the cold north, is not to go all the way south on the first go.
Some other tricks include:
Taking hot showers (and not cold showers); you trick your body into resisting the hot water instead of fighting the cold water. The hot water is still a great refreshment.
Having a shot of hot espresso. Similar reasoning.
Not getting out of the sea. In Greece, you can probably get away with not getting out of the sea for your entire life.
As a student, I've had free meals at the university. (Greek people love having things for free.) Even if a bit unsophisticated, these free meals actually gave me an idea about how the food here is like - different!
Other than having things free, Greek people also actually love having meat in their meals, which made culinary explorations a bit difficult to me. I've quickly learned to say έιμαι χορτοφάγος (pron. ime hortofagos), literally I'm a veg-eater - that quickly leads anyone: the guy at the pita-place, or the lady at the mensa, or your friend's mom, or whoever else is in charge of keeping you fed - to give you a double portion. Because, if you don't eat meat, you have to eat more other stuff. Twice more.
Wherever you'll go, you'll find people playing, performing music.
Jump on a ferry - meet a random band, one of the artist let me play his Cretan lyra. Go around the town, run into a rock band performing on the street. "The city won't let us organise a legal concert, so we're stealing electricity from that street lamp to power our amps." Enter a random club, a DJ is actually mixing some stuff live, not just juggling mp3's. Enter a cafe, and a noise artist performs with his laptop. Go to the local bar at the campus, or to the local squat - there's a gig or a d'n'b party almost every night.
As mentioned above, the illegal immigrants are a bit of a problem. I've heard stories from the locals, how you used to be able to leave your house with the door unlocked, and go about your business. The situation isn't making anyone happy.
The immigrants themselves are rarely interested in Patra or Greece, at least not at that point anymore; and did not come here to do anyone harm, but rather seeking a different future. It's just that: their current life situation. They've been promised dreams, they've paid with their entire families' lifetime's savings, they've been smuggled in through Greece's poorly protected borders, and are ending up here, bitterly disappointed.
In an effort to still make something out of this trip, they're hoping to hop on a boat to Italy. Jumping on one of those ferries continuously proves to be much more difficult than originally anticipated, so they tend to stick around - and with no language, and no jobs in Greece, they end up stirring trouble.
Strikes. Greeks love going on strikes. I don't know much about how effective these strikes are in getting whatever the particular group demands, but boy they are sometimes a pain in the ass to the rest of us. Bus drivers go on strike? OK, I can walk to the center, but not to Athens. Students force open the toll ramp and let cars through for free? Oh cool, we don't have to pay. (Greeks love having things for free.)
What happens when the garbage disposal service goes on strike?
Well, I went to the city center to have a coffee with a friend; worth noting here that the coffee is such an inseparable element of the southern lifestyle that the mere idea of not wanting one is normally considered absolutely ridiculous and a sign of likely mental disorder! When we both arrived in the area, we've quickly had a change of mind. I actually have witnessed a Greek person resigning from having the coffee.
Getting shit done is practically impossible. I'm not talking about the theoretical battle with the Greek tax system, which is apparently so complex that most people choose to pay the "just give me a break" tax that makes them exempt from a more rigorous control - because I've never had to pay my taxes in Greece and all of that were just someone else's horror stories.
But I had a taste of this bureaucracy! I was an exchange student, and your biggest challenge as an exchange student in Europe is dealing with, and bridging, two incompatible, foreign bureaucracies, and re-aligning them so that both actually work towards the original stated common goal.
Not much to add, I've failed here, as have many, many others.
I couldn't finish the song about such a wonderful place on a bitter note, so here's the final crescendo in D-Major: the island hopping.
If you feel like getting away from Patra, the best (not the fastest, not the cheapest, but absolutely the most beautiful) way to go around and see nice places is to hop on a ferry and go from one island to another.
Travelling around the islands is best done by 1. if you're rich, renting a car, or bringing one with you; 2. otherwise by hitch hiking. That's for real! The advice at the top of this story does not apply here; literally anyone will stop for you, both locals and tourists, if for no other reason, only because you're a curiosity on an otherwise quite dull spit of sand. Which makes the average wait time about 3-5 minutes; empirically, best possible in all of Europe.
Where to go? Anywhere in sight. Zakynthos is quite close and a must, from there you can hop to Kefalonia and from Kefalonia back to Patra or to Lefkada. Lefkada is considered by some as not being a "real" island, since there's a tunnel under the sea connecting it with the mainland; don't listen to these people and instead enjoy one of Europe's most beautiful beaches.
While in Igoumenitsa, you're both quite close to Albania, and in another international port city. See the above note on illegal immigrants, and consider not wasting your time on trying to hitch hike out.
If you're heading in the other direction (e.g. more around Peloponnese or towards Athens, which, by the way, are not that interesting), you can plan on visiting Crete, where you'll also usually have a lot of luck with hitch hiking. Try visiting Monemvasia as well along the way. The historical Olympia or Delphi are also both nearby.