We would like to make sure our tourist dollars really go to the local economy and not some big venture capitalists like AirBnB. What are the best places to book hotels or apartments? Also, what's a good itinerary for limited time?
I need more to go on. What are your interests? What made you want to visit? Where are you flying in from, and what times do you arrive and depart? Etc. Are you aware that early April is still winter there?
As for lodging, I almost always book direct with the hotels in Reykjavik because I know them and know which ones I want for each of our trips. I like the Center Hotels, of which there are quite a few. I also like Hotel Fron and The Centrum. As for lodging outside of Reykjavik, I almost always use booking.com since many of the smaller places do not even have their own booking platforms so they use this.