City property taxes are around 3% annually (of county assessed value). There is a 4% transfer tax as well (commonly split between buyer and seller). If you are moving into the city from outside it, be aware of the 3% income tax. (On the other hand, cutting your commute can save money and offset this, especially if you drive at $4/gallon.)
Remember there will be closing costs, including tax and insurance escrows, so your first year costs will be higher. You'll have to figure in maintenance costs as well; a home warranty is often a wise investment when you're short on savings. And make sure the home inspector is thorough. Ask to see a sample / blank inspection -- the best ones write long, narrative reports with pictures, as opposed to simply checking off boxes.
As for your specific question, it's tough for Realtors to answer, since Fair Housing laws prevent us from characterizing neighborhoods. http://www.callpittsburghhome.com/community_reports.shtml has community reports by zip code or school district (city/county as well). All we can really do is refer you to such third party resources and have you tell us what neighborhoods you're interested in. You should drive through them yourself (including at night), before looking at houses there with a Realtor.
A quick search of the MLS reveals over 60 2-bedroom single family or town homes (not condos) within the city limits, between $60K and $90K. These listings are all over the place, from north side to south side, east end to west end. There should be plenty of choices for you. Good luck!