I have came to the place using the public transport and it was quite easy to reach. The bus stop is just in front of the hotel. From the airport you need to change in Fira and look for a bus with destination Akrotiri or tell them the name of the hotel. The ride is about 30min.
The public transport time table/prices came in handy
http://ktel-santorini.gr/ktel/index.php/en/
The reception staff is very friendly and communicative, so if needed they can help you out.
The beach is quite close within walking distance and it has some trees, where you can take refuge at noon time. Good place for snorkeling and also you can do scuba diving on the same beach (55E).
The Red Beach is at 1km (20min on foot - return is uphill, so it takes about 30 min). There is no shade there, just a few places under an umbrella (which are of course taken first). On the way you can see the Excavation site (archaeological site diggings).
Please don't forget your sun/after sun cream and a cap! The heat can be quite high and you should protect yourself.
I've walked from Fira to Imeroviglis and Oia (read Ia). The path is amazing and you get to check out a lot of shops on the way. The streets and the city atmosphere is quite nice and cozy.
The sunset from Oia was amazing and a good place to see it is from the castle tower. Please keep in mind that the place will get quite busy as the sunset time is approaching. A lot of people will be there so it is wise to choose your seat/preferred spot.
The food is very good and is not very expensive (at least in Akrotiri). The bigger cities and specially Oia are more expensive, but not too high. The sea fruits are amazing, as well as the lamb.

If you're looking for ideas what to do I've found this website with a lot of good suggestions:"
http://santorinidave.com/best-things-to-do-santorini

I have taken the 7h volcano ride and I enjoyed it a lot. We've spent about 1.5 hours at the volcano, then at the hot springs (careful with your bathing suit as it will get stained from the rusty water). Then we left off in Oia the people that wanted to watch the sunset and then we cruised along the shore back to Athinios, the port where we departed from. The bus will be waiting there to bring you back to your hotel. The link where I've booked my trip is the following:

https://www.getyourguide.com/thera-santorini-l753/volcano-adventure-of-santorini-t46260/?partner_id=SOFBH69&cmp=santo3