I have chosen Boston for a weekend stopover while on a business trip. Where should I stay and what should I do ? Where is the best shopping etc ? Any help would be greatly appreciated.

Staying in Back Bay will be an ideal location. Plenty of hotels in that area, and accessible to the rest of the city by the T (Boston's subway system).

Not sure what to suggest you to do without know what your interests are. If you are interested in American History, you can very well follow the Freedom Trail. If you like art, the Museum of Fine Arts in Boston is excellent, and it currently has a "Gauguin Tahiti" special exhibit. Isabella Gardner Museum is another gem.

*Best* shopping- if you mean the high end shopping, Newbury Street in Back Bay, and Copley Place should suit your needs.

Are there any standout hotels in that area or others recommended? I'm happy with a modern hotel - Hilton-type or something equivalent to what The Algonquin is to NYC. Thanks for your help.

Your choices of hotels in Back Bay are:
Marriott, Hilton, Sheraton, Westin, Lenox, Eliot, Colonnade, Fairmont, + more...

Don'r forget the Ritz on Newbury St and the Charles something, I forget the exact name but it's almost across from Copley Station on Boylston.
Tell me what kind of shopping, High end or what so we can direct you .

I loved the Marriott Custom House! We stayed there last Septemeber and loved the location and the hotel!