I'm not aware of any bowling alleys, but there are two movie theatres close by. One is by Sea Pines Circle, the other is further away, across from the Pineland Station shopping center. Between the two of them, you have your choice of first-run movies.
Of course, there's lots of shopping; the Shelter Cover mall is close by and it's all indoors. Others are outdoor shopping areas, so you may have to run between the raindrops.
Adventure Cove is not too far away -- it's miniature golf (which won't help you if it's raining) but there's also an indoor video arcade. Actually, come to think of it, there's a new indoor arcade right at the mall.
We also have spent time at the Barnes & Noble bookstore when it's been raining -- although we didn't have a 3-year-old when we did that.
The resort is also good about trying to come up with alternative activities in case the regular activities are rained out.
One of our favorite things to do is just to sit on the porch of our villa and watch the rain. Rain at Hilton Head is better than good weather most other places!!!
There are many BBQ grills scattered throughout the resort, but not necessarily at each building. You never have to go very far to find one, though.
There are plenty of towels at the pools, but they're regular-sized, not beach towels. They work fine at the pool, but we prefer to bring our own larger ones for the beach.
Have a wonderful time!