There’s no “minimum” number of schools that you need to apply to. So long as you have at least one (and preferably two) schools that you’d be happy to attend that are extremely likely admits (or have already admitted you, ahem, Pitt), then you’re golden.
That said, if you are looking for some more schools, have you thought about Seton Hall? It’d be a likely admit and it has some interesting programming for international relations/diplomacy and links with the UN. It also runs its own program in D.C. If you’re interested in being in the NYC metro, it’s definitely a school to check out.
If you’re interested in government/policy jobs (rather than law school), I’d also take a look at schools in/around state capitals. These are some that might fit your preferred sizes.
- SUNY Albany (which would probably match your Penn State in-state tuition)
- Virginia Commonwealth (in Richmond)
- George Mason (VA), just outside of D.C.
- Ohio State
- Providence (RI)