April is usually a very pleasant month around here. The ocean water will still be a little cool, but otherwise a great time for outdoor activities. Definitely bring the bikes along. Murrells Inlet is part of the
Bike the Neck (http://www.biketheneck.com/ - broken link)trail. As far as beaches,
Huntington Beach State Park is about 5-10 minutes South of Murrells Inlet and has beautiful, uncrowded beaches. It also has a nice Education Center, nature trails and a great place for birdwatching.
Brookgreen Gardens is a little pricey, but it's a beautiful place and worth a visit. Also, a trip to Front Street in Georgetown, SC, about 30 minutes South of Murrells Inlet and the third oldest town in SC, can be fun. They have a small River Walk, some very good restaurants and a number of small shops.
Fishing is so-so. Surf fishing at Huntington is a good way to kill some time without much risk of being disturbed by the fish. The closest pier is in Surfside Beach, just a little north of Murrells Inlet. Veterans pier in Murrells Inlet also allows fishing, but April is still a little early for good fishing.