Warsaw

What exactly are you interested in? Sightseeing, bicycling, meeting locals?
The thing with Warsaw is, besides tourist spots there isn't much to see or do. Sure, you can go to pub, you can ride a bike somwhere, go for a stroll in the park, just usual things, nothing very exciting.

I don't drink dunkels so I won't be of much help, but if you're looking for wide variety of beers you can check out pubs like Kufle i Kapsle, Po Drugiej Stronie Lustra or Artezan. Artezan has more local beers, but I like Kufle atmosphere better. Are you going alone or with someone, though? Because I don't think sitting in a pub by yourself can be very enjoyable.
You can also check out Ojczysta Czysta, it's a place to drink vodka rather than beer, but they have great polish snacks to accompany it like marinated herrings or polish pickles.

As for the places, you can go to BUW, I don't think many tourist visit it. It's a Warsaw University library, very nice on its own and if you go to the back you can find an entrance to its roof, where you can find beautiful gardens and a great view of Warsaw.

Many locals spend nights by the river, drinking beer on the shore, but I don't know if the weather in October will allow you to enjoy that.

If you like nature you can check out Kampinos National Park, you can easily access it on bike, it's not that far away from Warsaw. And as for the bikes, there's a nice system of city bikes in Warsaw, you can rent one basically for free. Renting and returning points are located throughout the whole city, not further than 1-2 kilometers from each other, so it's very convenient.

I really like the atmosphere of Praga Północ, but I know many people won't agree with me. It's a part of the city that wasn't destroyed during the war, so many beautiful old buildings, churches and tenement houses are still there. And lots of great, traditional restaurants.

As for the food, do yourself a favour and don't eat in popular tourist restaurants like Zapiecek or any restaurant located on the old town for that matter. If you want to eat like locals, go to bar mleczny (but not Złota Kurka, it's awful and popular with tourists). They are very cheap (~10 PLN for a meal) and the food is actual traditional polish cuisine. You won't be able to communicate in English, though, you'd have to ask some other clients to translate menu for you or use some smartphone app.
Warning: staff will be probably rude and interiors are not very fancy or nice, but the food is worth it. My favourite one is Bufet Firmowy on Długa street.

If you haven't been to Warsaw before I do encourage you to check those tourist spots you're trying to avoid, there are popular for a reason after all.

I'm not polish but I have been to Warsaw. The old town is really the only nice place. Outside the old town it's more comparable to Detroit

The old town in Warsaw is actual one of the nicest places I've ever been to. Outside, eh, not so much