The only access to Mercer Island is by I-90: from the west, a pair of floating bridges connects Seattle with Mercer Island, and from the east I-90 provides access to the Eastside.
Luther Burbank Park is the most notable park on the north part of the island, followed by Pioneer Park in the middle of the island. The former park offers views of Bellevue and Medina, and has public docks, and the latter park is a nature preserve serving as a nexus for the many miles of trails throughout the island. There's a horse stables just south of Pioneer Park if you are in the mood for horse riding lessons.
Many of the greatest views can be seen from the smaller parks which dot the island. These include Groveland Park, Clarke Beach Park, and the westernmost edge of Lid Park, which sits on top of I-90.
Bennett's Pure Food Bistro is a surefire hit with all-natural and ethically grown and harvested food. It tastes delicious too! Most of the food and wine come from local growers and nearly everything on the menu is certified organic, even the all-natural Coke! They also have options for vegetarians, vegans, and special accommodations to those with allergies to certain foods.
There's also Thai on Mercer for Thai food, as well as Pom Proem Thai on 78th Ave.
Haruko's, Lil' Tokyo Teriyaki, and Yuzen round out the Japanese restaurants. Haruko's is a family run restaurant and offers standard Japanese cuisine. For more modern flare, go to Yuzen in the middle of the Island.
In addition to the above restaurants, there's a variety of small shops including fast food (McDonald's, Qdoba, Subway, Noah's Bagels).
Mercer Island has no hotels or motels to stay at, so if you need to find one, your best bet is to hop on I-90 either into Seattle or Bellevue, as both cities have multiple, varied options for overnight stays, assuming you are not a guest of someone who lives on the Island.