Open Air Wooden Architecture of Rus' Population of Podlachia Museum in Białowieża (Skansen Architektury Drewnianej Ludności Ruskiej Podlasia w Białowieży), ul. Zastawa 66B. Complex of wooden huts, windmills and other farm buildings. Also a chapel and a sauna. Most of the buildings are around one hundred years old.edit
Nature and Forest Museum (Muzeum Przyrodniczo-Leśne), Park Pałacowy 11, ☎ +48 85 682 97 04, . 9AM - 4PM Mondays closed. 12 PLN normal 8 PLN discount. edit
Palace Park (Park Pałacowy). An English garden park from 19th century. It assisted the (now nonexistent) palace located on the hill which Russian tzars used in summer while on hunts.edit
The town is surrounded by forest, which is the main thing to see/ do here. There are multiple well-signalled routes ranging from 4 to 14 km. One can hike through them, and some are also cycle-friendly - definitely worth a shot!
The yellow route also leads to a Bison reserve (8 zl, 4 zl for students with a valid ID). It's called Rezerwat Pokazowy Zubrow, and holds the most representative large mammals of the Forest, ranging from lynx and elk to, of course, the endangered European Bison. The latter are also part of a breeding programme that aims at repopulating viable habitat within Poland.
For nature walks with a guide you can use offer of Nature Tours "Pygmy Owl" Arek Szymura company - great experienced guides, full of passion for this forest  and whistling form Pygmy Owl by Arek is great.
Sarenka Cafe Gallery, ul.gen.Waszkiewicza 8, 17-230 Białowieża . A nice place, which sells art as well as hot drinks, fruit juice and similar (sadly no beer, wine or spirits) (the owner often organises live music, film screenings, impromptu feasts etc. Worth checking out).
There are many accommodation options in Białowieża village. From agroturism offers to cheap hostels or even more comfortable hotels are found. There's even a YHA youth-hostel there, yet it has been shut down as of April 2013. There are plenty of Bed and Breakfast starting from 50 zl.
PL Outback, ul. Graniczna 13, 17-230 Białowieża, ☎ +48 72 313 5666, . A new guest house with clean and modern double and twin rooms, all with ensuites. Shared kitchen facilities and lounge/terrace area. The owner Rose speaks excellent English. Well priced at 40-50zł per night per person. [firstname.lastname@example.org]edit
Chatka Puchatka, 6 Graniczna Street, ☎ +48 502 419 167, . Agro-tourism accommodation "Chatka Puchatka" is situated in a lovely quiet area far away from housing in the nearby Narewka valley. Five basic double-rooms with bathroom. An outdated website states 'regional breakfast and dinner or supper are prepared from local, organic products', though they no longer provide meals. The house is situated aback with panoramatic view of Bialowieza. The main tourist attractions are 15-20 minutes on foot away. It's possible to rent a bike and set a campfire.Per room approx €30 (120zł). edit