If you and your wife like to walk, Block Island has I think about 25 miles of hiking trails, and it's a free activity. Ask around, and you can get a free map on the island. I think the chamber of commerce building right in Old Harbor (near the ferry dock) has them.
My wife and I have walked there quite a bit (literally hundreds of miles over the years). I think the highest point on the island is only a bit over 200 feet, so you don't have to deal much with climbing.
Do be very cautious about disease carrying ticks (I wear a deet containing spray, light clothing, white socks, long sleeves,and tuck my pants cuffs into the socks). The island's deer population is enormous, and they (like all of Rhode Island) have quite a problem with lyme disease (and some other tick-borne illness, the name of which I forget). When we go on the trails we stay off any that are overgrown, and we don't wander into the brush. If your wife or you are anxious about the ticks, the roads can be nice for walking or biking this time of year. Some have more traffic than others.
The views are fantastic, and if you get tired of walking, the long sandy beaches on the eastern side of the island (Children's Beach, Fred Benson Beach, Scotch Beach, and Mansion Beach) are good places to take a swim. Obviously, don't go in if there is high surf and/or rip currents (which I think are a real possibility this weekend with the hurricanes out at sea).
Speaking of waves, a few years ago my kids and I took a ferry ride out on what my kids now refer to as the "vomit comet". I believe a hurricane was not too far out to sea. As a result, we now make it a habit before deciding to head out to check the forecast for the wave height and likely direction for the day going and the day coming home. This link
http://www.ndbc.noaa.gov/...ge.php?station=44097 will give you real-time data for the predominant wave height and direction of a buoy not too far from Block Island (it also gives some historical data)
During these walks we like to pop in for luch at the diner (I think it's called Bethany's) at the airport that's located in the middle of the island. It's one of the few places on island that isn't aimed at tourists. Their turkey burger's good, I like to wash it down with an ice cold bear.
Feel free to send me a message if you head there, I've got lots more info that might help you.