Between Logan Airport and Brewster Green...

...is there a recommended place to shop for groceries along the way? Thanks!

No. Go to Brewster Green and check-in. There is a binder in the unit on the coffee table in the unit with all sorts of information. There are three very large supermarkets within a ten minute drive of the resort (two Stop N Shops and a Shaws). When you go to the supermarkets head for the Courtesy desk and get a discount card, it will save you $$$$.
Brewster Green is a GREAT resort, the units are large and the staff are very helpful. I own two weeks there, if you have any more questions you can PM me. Enjoy.

Mike

You COULD stop enroute at exit 9

Egret,
If your intention is to stop at a supermarket enroute to Brewster Green in order to avoid an extra trip after your arrival (although it'd be a short one), then you could get off of exit 9 in South Dennis- there is a Super Stop and Shop right off of the exit and across from the Shell station. You will probably only be on the route 6 highway for a total of about a half hour to 45 minutes, and this is the most proximate supermarket to an exit on your route to Brewster. Once at Brewster Green, should you need to replenish your groceries you may find it easier and shorter to get to Shaws/Star Market in Harwich or the Super Stop & Shop in Orleans (imho, neither of these are as convenient to your route there.)
Brian

If you want to go shopping before you check in, take exit 11 off Route 6 (this is the exit for Brewster Green). Make a left onto Route 137, go about a mile and a half. There is a Super Stop N Shop on the left after the first traffic light. Check-in for Brewster Green is 5:00pm you may want to keep this in mind if you arrive on the Cape early and are buying groceries that require refrigeration.

Mike

Okay, since you offered....

....this will be our first trip to Cape Cod. We definitely want to rent bikes. Brewster Green rents bikes, I believe I saw. We'll need 4. Is BG the best place to rent the bikes? We're a family of 4, with two 14-year-olds. We enjoy beaches, dunes, hiking, biking, exploring; mostly anything having to do with outdoor activities. Although we all do enjoy museums and historical sites, too. We'll also be looking for a couple of good seafood dinners while we're there. Whale watching trips; Hyannis or Provincetown? Any and all recommendations, suggestions and thoughts are welcome.

When we leave Cape Cod, we're spending a week at Lake Placid; hiking, white water rafting, relaxing, visiting the Olympic Village. We've never been to this area either. Any recommendations or ideas?

Thanks!

Brewster Green is about a mile from the Cape Cod Rail Trail.
http://www.mass.gov/dcr/parks/southeast/ccrt.htm
You can rent bikes at Brewster Green and I believe you can also rent them on Route 6A near Nickerson State Park, the rental shop is on the Rail Trail. Also see this thread.
http://www.tugbbs.com/forums/showthread.php?t=65323

Mike

Thank you for the info

We look forward to the biking. We always rent bikes in Hilton Head. It's a joy to have nice biking trails to ride on.