The Museum of Prehistoric Thera, otherwise known as simply the Archaeological Museum is located in the capital
Fira. It's right on the main road just to the south east of the old harbour.
The artefacts housed here were discovered in excavations on the island with various pieces dating back as early as the 5th century BC.
The museum of prehistoric Thera consists of pottery, sculptures and mosaics with information signs to let you know what everything is, when it was made and where it was found.
Some say that the exhibitions are a bit basic and the museum in general is too small to make it worth your while visiting but the entrance fee is just 2€ so if you're in Fira anyway then you might as well have a look for less than the price of a beer.
The opening hours for the Archaeological Museum are between 8.30 and 15.00 every day except for Mondays when it's closed all day.
There's a car park opposite and a few others dotted about the town but parking can be difficult in Fira so the bus or a taxi may be the easiest option if you're visiting from outside the capital, especially as the bus station is just round the corner. If you can't find a space in one of the towns car parks then you can park on some of the streets around Fira but again it’s hard to get a space.
If you enjoy museums, historical artefacts and archaeological sites then other options are
Ancient Akrotiri and
Ancient Thera, there's actually a 15€ pass that gets you access to all 3 sites so if you plan to visit all 3 be sure to get that pass and save a few euros.