You might like the Residenza Carducci B&B
http://www.venere.com/bandb/verona/resid… It's just across the river from the old town in Verona - in walking distance to everything.
Generally, when I stay in Bologna, it's close to the airport or the train station. You might be more interested in something close to Piazza Maggiore though. The Best Western San Donato could be a good value and meet your other criteria:
http://www.venere.com/best-western/bolog…
Hotel prices here in Italy vary a lot depending on what's going on. bologna is a city of trade shows so prices and availability will depend on exactly when you want to stay. While you're in Bologna, you might try the Ristorante Montegrappa da Nello - it's a great trattoria about a block from Piazza Maggiore that features local foods with very fresh ingredients. They had a big basket of beautiful Porcini mushrooms Saturday night and were making a lot of specials featuring the mushrooms. The tortelloni verde montegrappa with porcini slices was excellent. It's also very reasonably priced. If you go up the left side of via dell'Indipendenza from Piazza Maggiore, it's just around the corner of the first street. Sit outside if the weather is nice.
In Verona try the Alcova del Frate in Via Ponte Pietra - it should be perfect for the two of you. Ristorante Greppia is another good choice. There are lots of possibilities in either city as you'll see just walking around.