I am in the Wills Memorial Building on Queens' Road, just before it becomes Park Row/Perry Road - so not far from where you'd be at all.
As Carrie said, although Clifton is a lovely area, it can be very expensive (I just saw a 2-bedroom flat in Clifton on the market for £320,000, which is almost triple what my parents paid for our 5-bedroom, 2-kitchen, 3-bathroom house in South Gloucestershire, north of Bristol!).
To start with, I would look for places to live North/West of the campus - Cotham and Redland are fairly nice areas close to the university. Redland is about 20 minutes walk from Park Row, although many people do cycle in. The university is not technically on a campus, so you may be able to find accomodation within the university precinct, although there may be high competition for housing in the area.
My list of areas to avoid includes the St. Pauls, St. George, Easton, Montpelier areas as they have high crime/drug rates compared to other areas and are not so pleasant to live in. I personally favour the areas of north Bristol rather than south Bristol because I live 15 miles north of the city and rarely go further south than the university and city centre, unless I'm travelling down to Somerset.
Public transport is good in the city, but it can be expensive - if I were to take the bus into my department, it would cost me double what I pay for gas to drive in!
There are quite a few summer leases available from June/July-Sept, if you wanted somewhere live to start with, although I'm not sure if they are only available to students or not. Otherwise, I don't know how easy it is to find a flat in July.
I hope some of this helps