Windows facing only the east

East-facing windows get only (direct) morning sunlight. Depending on how high up you are, you might get more or less sunlight. Overall, east-facing windows get less sunlight than south-facing ones. Hence, south-facing windows are preferred. But it should be okay. There are many factors to take into account in a rental, so my feeling is if you are not certain, don't jump into it. Take your time. Dark floors can also be depressing. Whatever reservations you have now about the apartment will continue to be there once you have moved in. So .. east-facing windows are not a major problem in itself. Avoid at all cost north-facing windows, you will be depressed and miserable, esp. in the winter when there is little sunlight.

Keep in mind that east-facing exposure will also mean the sun will come shining in early in the morning--if you want to sleep past sunrise you'll need black-out shades.

I prefer North and East exposures. South and West gets oppressive sun in summer. My current place faces East. I wasn't sure I would like it but I do. It gets dark a little sooner than my old North faceing place.