The city of Nikiski is an oil town. Almost everything there is focused on serving the offshore oil and gas industry. Unlike every other town in this part of Alaska, there are very few tourism based business or attractions.
Nikiski is accessible by road via the Kenai Spur Highway. The airport is a single gravel strip with no scheduled flights. The next nearest airport is in Kenai. Due to being an important port for the oil and gas business, marine access is restricted and there is no public use harbor. You can rent a car or get a taxi in Kenai or Soldotna.
You will almost certainly want a car. Nikiski is not pedestrian or bike friendly, and there are areas near the fertilizer and natural gas plants where stopping your vehicle is prohibited. These areas don't smell particularly nice either.
To get here by road from Anchorage you will have traveled through some of the most spectacular scenery on earth. That's all behind you in Nikiski. While you can still see the mountains on the other side of Cook Inlet from here, the main thing you will see is run down strip malls, abandoned hotels, and giant petrochemical plants, that seem very out of place in coastal Alaska, but serve as a vital economic engine for the local economy.
However, if you just keep driving for another 25 minutes or so, you will reach a very nice recreation area, detailed in the next section.
Due to its large tax base from energy development, Nikiski has more infrastructure than one might expect for such a small, relatively isolated area. In addition to the building of new schools and the purchase of new fire trucks and rescue boats, Nikiski also has a publicly-owned indoor water park and pool that you can access for a small fee.
About fifteen miles past Nikiski, at the very end of the Spur Highway, is the Captain Cook State Recreation Area. This park has a large wooded campground, a lake, and long beach along the shores of Cook Inlet. The campground is regularly visited by bears; do not leave food or beverages unattended at any time. There is also road access to the beach, but it is not recommended to drive on unless you have four-wheel-drive, high ground clearance, and experience driving on both deep sand and large rocks. Tides in Cook Inlet can be extreme and you may need to head to higher ground as the tide comes in. There are mudflats in this area during low tides. Do not enter these areas as they are extremely hazardous to all pedestrians and vehicles. If you become stuck (which you will) the tide will eventually come back in and flood the area.
The park is also the terminus of the Swanson River canoe trail. The River offers fishing for salmon on the summer months.
There are also several public lakes in this area with decent fishing for dolly varden and other trout species. While the access is public, the other land around these lakes is private, and in most cases well populated. The fishing is good but the view is of suburban backyards and the occasional teenager on a jet ski. Stormy Lake, in the state recreation area, is the exception. It is a large lake, with a primitive campground on the far shore that is only accessible by boat.
Since you are almost certainly coming by road, your best bet is to get whatever you need at the many stores in Kenai and Soldotna. There are convenience stores and gas stations here but that's about it.
Again, do this is Kenai or Soldotna.
You will probably want a drink when you see this town.
There are no hotels in Nikiski that one could recommend to anyone. There is camping further on at state recreation area.
The way you drove in is literally the only way out unless you hire a local pilot to fly you somewhere else.