It's just after 8:30pm, and the sun is still a good deal above the horizon. Can I really call it sunset? I'm not sure, but with the midnight sun in Iceland, it never really truly gets dark. It's kind of a weird phenomena.
On the upside, your touring day can be as short or as long as you want since you always have a good deal of light available. Things do close, but nature is still open for business. It can be a bit eerie at times if you're out at say 12am, taking photos when no one else is around an otherwise busy location. Then again, you're out at 12am because you want to take photos when no one else is around an otherwise busy location!
There's not a whole lot to see and do in Akranes, besides this lighthouse. For me, it was a place with a few more dining options than some others villages in the region, and made for a nice stopping point for me that day. A visit to the Akranes Lighthouse was my post-dinner stroll.
If you're off to explore more of West Iceland, there's an undersea tunnel connecting Reykjavik and Akranes that shaves off a good 40 mins or so of driving. I generally found it to be quite pleasant to drive anywhere in Iceland, except for when I got closer to Reykjavik. Then there were more traffic circles to deal with, which posed a challenge for me as a new stick-shift driver not yet confident in my manual driving prowess.
Overall, the lighthouse is one of those 10-15 min stops. It's unlikely to be a place you're going to spend an hour or so exploring - for which, Iceland is filled with those. If I was short on time, I'd definitely choose a waterfall or volcano or any number of crazy amazing natural sights that are so common in Iceland over a lighthouse. If, like me, you just need somewhere peaceful to wind down your day, a visit to the Akranes Lighthouse is a nice way to catch the "midnight" sunset.