I am looking for a place to stay in Rome for four nights. Two adults and two kids (10 and 8 year old)

Day 1: We will fly in FCO and take an airport bus to downtown. I took a bus from Termini station to FCO last year and it was very convenient. We are okay with walking up to half mile (800m) with bags.
Day 2 and 3: City Tour
Day 4: We are planning to join a group tour to Pompey. The tour bus starts at SIT bus station, Via Marsala, 5, 00185 Roma RM
Day 5: Train/Bus/Airplane to Bari, Italy

Since group tour starts/ends near Termini station, I think booking a place near Termini is ideal. However, I am okay with taking a short taxi ride.

We are looking for a place with at least two beds (preferably two beds, not including a sofa-bed).

In USA, we usually book a hotel room with two double beds. I am not sure it works this way in Europe. I notice many website limits three people in one room.

We are okay with (with a kitchen or without a kitchen) But having a kitchen would be nice at the same price.
My budget is 150 EURO per night.

Thank you for your advice.