As Hyde Park is so dominated by the University of Chicago, I'd suggest getting some info from local residents. Walk around the neighborhood, talk to baristas in cafes, just ask around. You'll find out that awesome apartment with low rent is really in a crazy loud building or really just as great as you dreamed. Then check around on Craigslist. Hyde Park is a safe neighborhood, you'll find some good people putting their apartments up for a reasonable price.
There are a lot of great resources out there for finding an apartment in Hyde Park.
Craigslist.org has a great section for rentals and most of these are rentals by owner.
Trulia.com is also a great resource - you can select your neighborhood, what amenities you want and even put in your minimum and maximum you are willing to pay per month.
Another source I would recommend is ApartmentHomeLiving.com. It allows you to choose your state, city and then neighborhood. It has a lot of the same features as Trulia with the ability to choose amenities and prices.
Here are a few more you can try: ForRent.com, Rent.com, WalkScore.com, MyNewPlace.com, and Zillow.com.
I particularly like WalkScore.com because it gives you great information on how 'walkable' the area is, what your commute time will be and if you are near transit.
You can also use the local papers and most of them have an online presence now where you can look for apartments that way too.