We have stayed at a number of the Center Hotels and really like them. Center Hotel Plaza is one that we have stayed at a few times, and are booked for again in March. I love the location as it is right smack in the heart of town. Hotel Fron is another very good hotel right in the heart of things, and the Centrum as well. We have had great stays at all of these, plus a few a but further. We have not had any issue with noise at CHP, FWIW.
From the airport to Reykjavik, the Flybus is what many people take. It is around $39 pp each way. You don't need to reserve it as they leave when the bus fills, and they are there after every flight. They take you to the central bus terminal and from there you transfer to a smaller bus that is allowed to go into downtown and they stop around various bus stops. A taxi is an option as well, and one that we use most of the time if we are not renting a car. A taxi is about $150 US dollars each way, but it is door to door so it is very easy.
For day of arrival, you could do the BL and then head into Reykjavik, or do Sky Lagoon which is in Reykjavik. Both are good. For arrival day I highly recommend the Citywalk "free" walking tour (tip at the end). You can only book about a week in advance and it does sell out, so note it on the calendar if you are interested. The food tour is excellent as well. The is about 3 hours and there s plenty of food for lunch and dinner. You could also hit a local pool that evening.
For your open full day, I would skip the Golden Circle actually, and either do a full day tour to Snaefellsness or the south coast. Both are great and have much more to see than the GC does. They are longer tours though, but IMO, worth it.
Since your flight out is very early, you might consider heading back to KEF in the late evening and staying at the Aurora Hotel. It is literally a 5 minute walk across the parking lot to the terminal, and that would give you a bit more time to sleep in the morning.
