Driving down the Seward Highway around Turnagain Arm is one of most scenic drives in the world. But better than driving is biking it. At this time, about a 1/3 of the ride is actual bike trail and about 2/3 is the fairly wide shoulder of the highway. The section into Girdwood is the old part of the highway up on the mountain ridge and is closed to motor vehicles. The first time I biked this, it was one of the most awe inspiring things in my life. If you have the time, I totally recommend this as an activity.
You can take any section and bike as long as you like. However, the best part is between Bird Creek and Girdwood. Start with the bike trail just before the Bird Creek Campground.
In 2005, major construction was completed between Indian and Bird Point. Consequently, a bike path was installed connecting the 2 existing ones above so you no longer have to ride on the shoulder.
If you're up here with the intention of doing a lot of different things, I would put this high on my list. There are many places in town that rent bikes and the cost is not outrageous.
While the shoulder is wide, wearing a helmet is still strongly recommended, as you are on a major highway.
Turnagain Arm can get mighty windy. Be prepared you may have to burn some calories to move along. Bring a windbreaker and wear synthetic clothing that wicks sweat to avoid chills.
Warning! Under no circumstances should you ever walk onto a mudflat. It is very similar to quicksand and you will find it very hard to remove your feet from the mud. With one of the fastest tides in the world, you're looking at a deadly combination.
If you decide to stop at Girdwood, go the extra couple of miles up the road to a really great bakery. Even further up is the Alyeska Ski Resort.
The Bird Point Rest Stop is worth taking a break at as there is a great interpretive installation on the ecosystem around the Arm as well as a really cool beaver dam nearby.
Turnagain Arm, including the Cook Inlet, is the 2nd fastest tide in the world (after the Bay of Fundy). Check the tide tables (available at any bank) and time your bike ride as high tide starts coming in. Trust me on this.