Sure you can get an Über. We took a cab and it was 18 USD as I recall. So an Uber is always cheaper

Children would be bored.

Either start or finish at The Liberty Hotel on Charles Street (at the beginning of the Longfellow Bridge, where the Charles / MGH T station is). It is a luxury hotel set in a converted jail, where many of the features have been carefully preserved. The main feature being a soaring 90foot ceiling in the Atrium and the cell catwalks and wrought-iron work from its 1850's construction. It's 3 minutes' walk from the Charles River Esplanade, and 4 minutes from Beacon Hill's boutique shops and restaurants on Charles Street. If you have time, detour up to Acorn Street for a bit of cobble-stoned history.

Boston is a very walkable city. You can either walk there and experience some of the Freedom Trail, or you can catch an uber. Depends on your level of fitness and whether you will have all your suitcases with you.

I lived in Beacon Hill for three years! The best way to get there is to take the Red Line (going to Alewife) to Charles MGH 'T' stop. Go out of the station and walk onto Charles Street. Beacon Hill is on the left. It is an area with lots of picturesque streets leading uphill from Charles Street. You could get off the Red Line at Park Street 'T' and walk across Boston Common to Charles Street in which case all the picturesque streets would be on your right but it is quite easy to go the wrong way across the Common!!