Yes, I think going to the city was worth it. The airline magazine says the Islamic Art Museum is open until 10PM. The guy at the information desk at the airport said until "about 9". The actual time is 8 on Thursday, Friday and Saturday, earlier the rest of the week. So I only had about 30 minutes but that was enough for me.

The visa was $27 and you swipe your credit card when you go through immigration.

The taxi going into the city was 34 riyals. Coming back, the driver took me on a circuitous route and it came to 58, which I didn't pay. If it's more than 35-40, then you are being ripped off.