Mollie
New Street Station is the one for you.
London Midland will get you there from London Euston in a little under 2 and a half hours. Its generally cheaper and stops a bit more. You don't have to change trains but you can change in Northampton if you like. Trains run at up to 100 mph, a small first class area with electric plugs and tables and curtains, no catering, and lots of standard class seats. Reservations are available but not for specific seats. Huge picture windows allow easy views of the spectacular scenery.
Virgin trains will do the trip in about an hour quicker with fewer stops, travel at up to 125 mph, tilt, have electric plugs at all seats, in first class serve food on china for a price, in standard have access to a buffet area (you don't get a buffet, its more like a counter in a shop), smaller windows not always lined up with the seats, and are generally quite a lot more money.
Both are good for the niches they fill.
The hotel you will be at is near Gas Street Basin which is a highly picturesque narrow boat marina on the 250 year old canals. You can walk down the tow path next to the canal to quite near the museum.
That's below street level. On street level, Broad Street is a street of restaurants and bars, with the emphasis on bars into the evening and weekends. A little down at mouth because due to the recession fewer people go out and spend less money.
Around the canals are thriving areas of other restaurants and bars, less emphasis on bars.
At the far end of Gas Street Basin is The Mailbox, with posh shops and restaurants, emphasis on posh.
You could walk through The Mailbox to the side exit of New Street Station if you knew the way and didn't have luggage, but there are lots of stairs on the way. That's probably the 10 minutes the hotel mentions. I'd take a taxi from the front of the Station when you arrive until you get your bearings. With 4 of you and luggage that's probably best.
good luck and enjoy
