Stopping at Tern Lake at the junction of the Sterling Highway and Seward Highway is a must. It is a popular picture taking spot because it is very accessible, and the lake is in a nice valley with mountains all around. The mountains in this picture are looking toward Seward.
Map Reading: You will probably notice that the highways in Alaska are named and numbered and either can change. The Seward Highway would be the stretch of road from Anchorage to Seward, but Highway 1 turns down toward Homer at Tern Lake is called the Sterling Highway from this point on. In the contiguous lower-48 changing highway names and numbers could make it really hard for someone unfamiliar with the territory because there are so many options. But in Alaska, there are only a few major highways and the signs are well-placed so it is hard to get lost.
It's spread out, and the area comprises two towns close together--Soldotna and Kenai, with smaller ones nearby. Driving is an absolute must, unless you're truly hardcore and can bike over a 100 miles a day. There is no local bus service that I've ever seen.
You can take a boat to explore the beautiful coastal areas and fjords of Kenai Peninsula. They are available at the seaside towns e.g. Seward, Homer, Whittler.
Most people visiting Kenai would either come down by train from Anchorage, or they may come by ferry to either Seward or Homer.