For our yearly vacation in April, my husband and I stayed a week in Cape Cod at "The Harwich Port" in Harwich Port, MA. A friendly and welcoming place, the timeshare offered relaxed and private accommodations. The Harwich Port is located in the center of the quaint town of Harwich Port, just steps from shops, restaurants, the post office and three minutes by car to the star market (which was GREAT). Across the street from the inn, down a short bike trail, is a beautiful public beach. While in the area, we enjoyed touring the fishing towns nearby, playing mini golf (Cape Cod has the most mini golf courses per capita in the US) and riding along the well-marked bike paths.
We took the ferry to Nantucket one day, and spent our afternoon riding bikes along the island. There are two bike rental shops located right off the ferry that are reasonably priced and convenient. These rental shops provide free bike trail maps of the island and will give directions if you ask.
Since April is considered "low" season in Nantucket, not all the restaurants and tourist shops are open, but there are enough to keep one occupied for an hour or two – three to four hours if you are a "serious shopper." On the positive side, low season also brings peaceful, quiet trails - empty beaches free of crowds - and natural beauty including daffodils, along the roadsides and bike trails.
Towards the end of our trip, we spent a day driving through Provincetown (the roads are very narrow) and sightseeing in the national parks on that side of the Cape. Note: It can be quite cool and windy during this time of year, so make sure to bring sweatshirts and/or windbreakers and hats for outdoor activities.