I live in a tiny apartment on the 4th floor, narrow stairs and no elevator. I'm looking to buy a bike, and planning to put in 50-60 miles a week at least. Could you recommend a bike in the 300-350$ range? It would be better if it is a foldable bike
Downtube has a a sub-400$ folding bike, the 7sp.
Dahon also has a few sub-400$ folding bikes: the Boardwalk S1 and the Speed Uno.
However, if you're planning on doing longer commutes, I would suggest folding bikes with larger wheels, like the Montague Crosstown. These bikes are, however, a bit more expensive, but offer a much more comfortable and speedy ride.
I'd recommend getting a cheap used aluminum frame bike (a beater), a good lock, and a bottle of oil. Then, I recommend you lock it on the street most of the time. I recommend cheap so that you won't worry about it while it's parked on the street. I recommend aluminum so that it is light enough to haul up to your apartment for those extended periods when you won't be riding it (also so it doesn't rust).
It might take a beating getting stored outside, but if you ride it frequently that'll battle the effects of the weather (as will the bottle of oil). One of my schools (in the midwest) had nearly 100% outside storage for student bicycles. It snowed, rained, etc. But, as long as the bikes were used and maintained regularly, they ran fine. (The ones that sat for a long time eventually turned into piles of rust.) If you spend, say $150 or so, you'll have enough left over for periodic tune-ups on your cheapo from your local mechanic.
Also, if you store it outside, you'll be more likely to ride it for quick trips than if you have to haul it up and down 4 flights of stairs.
How tall are you? I am 6'1", but I have a boy's mountain bike with 24" wheels, which I got used six years ago for 80 dollars. This is fine, because I raised the handle bars as far as they can go, and for eight dollars, I replaced the seat post with a much longer one. In all regards except size, it's a normal mountain bike with a decent spring-loaded front fork, good wheels on aluminum rims, good V-brakes, good derailleurs. A few incredibly cheap and easy modifications turned it into what is de-facto a small-form-factor adult bike.
Boy is this bicycle ever handy. Though it doesn't fold, it fits everywhere I need it to. It does very well on crowded commuter trains, and inside small elevators, escalators and stairwells.
The 24" wheels are more than large enough for distance road use. I go all over town on this thing. Ten miles each way to work and back, plus evening and weekend outings.
Used bikes like this can be found in decent shape. Kids can be rough on equipment, but not in the way that grownups are. I mean, a kid's bike will not have been used 30 miles a day for commuting to work, in inclement weather. Plus, one reason these bikes may be sold on the second hand market is simply that they were outgrown, not necessarily because there is anything wrong with them.
After my experience with this bike, I never want anything larger.