I normally wouldn't live in a place without some natural bodies of water: rivers or lakes or sea, such things. Despite that, I've managed to survive almost two years in Łódź.
It's a big city, however many uninitiated say there's about only a single interesting place there: Piotrkowska. That's far from the truth!
Park Poniatowskiego also has an old bunker complex underneath, the entrance usually being sealed. Be careful if you go inside!
There's a lot of old and ruined buildings scattered around the city. (20th century old, not medieval old.) Most are semi-safe to enter, but exercise caution.
If you find yourself around Piotrkowska, or in Manufaktura, you should try Green Way. Cheap, yummy, and all veg. Smaller streets branching off Piotrkowska are also full of vegetarian restaurants.
While Poland is often perceived as xenophobic, you won't have much trouble communicating in English in Łódź; in fact, you're also likely to run into other foreigners, visiting or cohabiting.
I was pleasantly surprised to find the locals a very kind and helpful bunch of people. It's not England, but the difference is noticeable if you contrast it with the rest of the country.
You'll also find that Łódź has - not entirely a dialect, but say a distinctive collection of slang words for some common terms; migawka is the monthly public transport pass (standard Polish: bilet miesięczny), or krańcówka for the final stop.
The Public Transport
Some of the country's oldest functioning trams are still occasionally in service, and that's absolutely not due to the lack of funding (most of the fleet is actually quite modern) - check out the KMST (Old Trams Enthusiasts' Club; also old KMST website with info in English).
There's also the Europe's longest tram line, 46, which runs all the way from Zdrowie through Zgierz to Ozorków. Yep, that's correct, it actually passes through another city. The trams running the line are also quite vintage.
Do buy the ticket. It's cheap, every tram has a ticket machine, the inspectors are a pain, and the fine is high.
No, Łódź doesn't have underground public transport (yet).
Start easy, check out the web page for the Sewers Museum "Dętka" (scroll down a bit). Go visit! Like it? There's more! But it's pretty hardcore, and actually not quite legal.
You can always go through a manhole, however it's difficult to find one that leads directly to a bigger corridor. It's easier to just find a proper entrance.
One of the interesting entrances is located near the bus stop Pienista - Obywatelska. Take the bus 65 towards the airport. Get off at Pienista, continue to Denna. Follow the foul smell. There will be two entrances - follow the one that smells a bit less gross - it's for rainwater, but it will later merge with the sewers and lead you to Lindley's chamber, situated near train station PKP Kaliska.
Be prepared for a rough march, it's about 2-3km and the first part of the corridor has a pretty low ceiling. Also consider that you might have to go back the same way - lifting the manhole lid is much more difficult than it looks on the movies! Especially since you'll need one hand to hold on to the ladder; especially since you can never be certain where you'd get out and if a car won't run over you.
Beware that this is not exactly a safe sport. It's actually life-threateningly dangerous, even if you're not a total moron. Take a friend with you. Don't do it if you're not sure. Inform someone about the trip, have them await an update. Consider that the mobile network coverage might be very poor, or even nonexistent. Consider bringing some eye protection - your eyes might start to hurt after an hour or two. And most importantly, check the weather forecast and confirm that there's zero rain expected - you don't want to get flushed!
Take a good, long shower afterwards!