Suceava is cool to visit. it was a capital city many year back, when Moldavia was an independent state (now, Moldavia, Transylvania, Muntenia and Dobrogea contitute one state, Romania... we speak the same language.. so no big fuss about that)... anyway... suceava has a few places to see, but should be included in an area program, meaning that it doesn't take that much to visit and you'd want to head out to the monasteries which some compare to the Sistine Chapel due to their paintings which are quite unusual... i found them fascinating although i'm not religious.
hostels are cheap there, i know some people in suceava so just ask...

You can find near Suceava famous historical places of North of Romania, like the Monasters in Tumor, Moldovita, Sucevita etc.

Boring city, still in Soviet era style But around it are wonderful unique monasteries of the 15-16th cent which are in the UNESCO world heritage list with extraordinary external walls painting

couple of nice orthodox churches. calm and quite on weekends.