My wife and I lived around the area for 6 years for school and still at times miss it.
Depending on what type of living you like (i.e. complex vs. apartment in a house), there are a great many choices.
Originally we lived at Elmwood manor as suggested by a different poster as we were afraid to live in the city. It is a nice complex located close enough to thoroughfares to
commute. It seems to have a more "yuppyish" crowd. Brighton/Pittsford are considered some of the "nicer" (read higher rent) areas. Webster/Fairport/Penfiled are considered safe, slightly lower cost east side suburbs, but you will have to commute, as much as it is, with the flow of people.
About three miles from Elmwood Manor you can live within city limits in apartments in older homes in the city (read student, as well as young urbanite areas). We absolutley loved our time in this area (areas referred to as Swillburg, South Wedge, Meigs-Monroe neighborhoods.) Rents are typically lower, and we personally love older houses. If you have ever lived in a city, you should be fine in these eastern city neighborhoods. If, like us, you were from out in the country, you may want to live in the Brighton/Pittsford areas before finding out which neighborhoods/streets are better than others. In Rochester it really can be street to street and time of day dependent on how safe you may feel in a particular area; I wouldn't get lost in the city at night at first. We found craigslist to really helpful in apartment hunting.
Make sure you check out the Public Market, one of the best open air farmer's/produce markets we've seen, as well as the famous garbage plate. There are also lots of outdoor recreation opportunities if that's up your ally.
If you have any other questions in addition to my long-windedness, feel free to message me.