Nigel: I didn't have luck staying near the train station, a combo of too many people in a room (2 adults, 2 small kids) and last minute booking. Ended up having to take the tram to the Bern Novotel but all worked out. However, like the others posted, hotels close that I would look into again next time--National, City, Continental and of course the Hotel Schweizerhof (super pricey though). The National would be my top pick, although they received mixed reviews, the location is ideal, off to the side and right by the tram line if needed. We ended up walking from the US Embassy back to the Novotel which was not bad and a great way to see the town. My two kids (ages 3 and 8) were fine with the walk and stops along the way to play.
Thank you all for the help!