VanillaChaiTeaTime

No need to thank me, I remember how difficult it was to figure out the details of the move.
 
For the off-campus housing finder, I believe you can sign up for the site as an incoming student, you just choose "guest" rather than "UConn Student" under the sign up options.  
 
Something to be aware of in terms of how quickly places fill up, the university announced a few weeks ago that they would no longer be providing on campus housing for graduate students. Not a lot of graduate students choose to live on campus, but removing the ones who otherwise would choose to do so will make the housing market a little more competitive. In my experience, most incoming students won't start moving to the area until closer to the end of the summer. Moving out a little bit sooner (if possible) would help you beat the rush.
 
Also, another potential housing option is The Oaks on the Square (http://www.theoaksonthesquare.com/index.php/prop/home). These units are very close to campus (walking distance close), in Storrs Center where all the construction is currently going on. I personally think they are too expensive, but I thought I would let you know just in case you were interested. 
 
Again, feel free to ask me any questions. I had a lot of help from various graduate students and professors that made my move out here a lot easier than it would have been otherwise, so I really try to help out other students whenever I can.

Yay! Welcome to UConn! What's your program?
 
It sounds like you have a car, so you have more options than you would otherwise.
 
I know some students live in Vernon, Manchester, Stafford Springs, and Hartford as well as Willington. Hartford tends to be pricier because its the city, and its a bit of a drive. I've heard good things about Vernon as well, but I don't have any personal experiences to draw from.
 
A lot of students live in Willimantic, myself included, because there is a bus line to campus. Even though you have a car, you should be aware that parking is a nightmare here, so having the option to take the bus sometimes could be an advantage. However, Willimantic is a lower income area, I'm sure you are aware with some of the issues that go along with that. Overall I like Willimantic, but there is not a ton of stuff to do. There is a nice legitimate non-Starbucks coffee shop/cafe and an awesome microbrewery (great food and beer). Willimantic is also only about 5 miles from campus as well, so the commute's pretty good.
 
You might want to check out Colonial Townhouse Apartments (Its in Willimantic/Mansfield). I only suggest this place because I know they do allow pets (with deposit) and the rent is pretty reasonable (750 for 1bd). You've probably already found this, but I found my apartment using the uconn off campus housing finder (http://www.offcampushousing.uconn.edu/). I would recommend starting there to see the most commonly populated areas/available places to rent.
 
Hope this helps! Let me know if you have any other questions.