Not much bike-wise around that I remember. A general walk around the new-old town is a nice way to spend the day and there are some great restaurants that’ll fill your plate with some tasty fresh meat (not a euphemism). I wouldn’t bother going up the mini Russian Empire State building as there are generally massive queues and nothing really exciting to see on the skyline but probably worth saying you’ve seen on a wander past. The Royal Park (?) is also nice for an amble.
Assuming you are central, maybe start at the Palace of Science and Culture, walk up Nowy Swiat (there was a cracking restaurant there whose name escape me but there is a butchers inside on the right), bimble around the new-old town and take the scenic route back through the Royal Park. Nothing stood out for me about Warsaw but it was alright for a general mooch around taking in the sights
