There are lots of taxis driving around. The city centre is small so you dont need a taxi for that. To get top the cemetery, bus- or train station, take a taxi. In Botosani, taxi drivers will probably use the meter but ask just to make sure. Taxis are not expensive for western standards.
It is also possible to take a taxi to Suceava; it will cost about 14 euro (500000 lei).
There are about seven daily busses from Botosani to Suceava. The bus was better then I would have ever expected. Very comfortable and clean.
The trip costed about 1 euro.
From Botosani, there are busses to lots of Romanian towns and cities, among them Iasi, Bucharest and Tirgu Mures.
There is a daily direct train from Bucharest to Botosani. It leaves little after 11 AM from Bucharest Gara de Nord. The trip takes about seven hours; it is a rapide train, it only stops in the bigger stations.
A first class ticket costs about 19 euro, a second class ticket about 12 euro (including seat reservations).
There is also a night train which we didn't take.
There is a tram line in Botosani. It connects the city centre and the railway station. We didn't use it, but it might be an alternative for taking a taxi.