My tip for you's that cost is negotiable. I ended up apartment searching last-minute too, August for a September lease, and since landlords were desperate to move places I was able to get some bargains! We ended up in a 4000/mp apartment for 3100/mo. So feel free to make an offer a couple hundred bucks lower than asking and see what happens, especially if you're not working with a huge apartment complex kind of place. I don't think people will be as desperate to get rid of apartments for a June lease, but you can still see if there is any leeway in rent.
Also, you can live cheaper if you find roommates...
And, be sure to check out the neighborhood/street you could be living on. there are sites where you can see how much crime occurs in each area... if you aren't sure about the neighborhood, look it up. don't live somewhere unsafe just to save a little money.