You can take a bus from Tirana to Sarandë but since it departs early in the morning, you may try getting first to the town of Vlorë and then taking a bus to Himarë. If you arrive from Corfu through Sarandë there are regular buses from Sarandë to Himarë (despite what taxi drivers may claim).
The most reliable way to get around is hitchhiking. Basically, any car with available seats and heading for your direction will take you. If you still prefer a taxi, call 068 418 08 72
If you go for a stroll through the Himara Castle grounds (starting at the parking lot), at some point you will see a small sign saying 'coffee'. Follow it to a beautiful house where you get to sit on a balcony overlooking the sea. Ask for a frappe/ice coffee, you won't be disappointed.
There are a couple of hostels in Himara, among them:
All of them charge around 10 euros/night with breakfast included.
There are several hotels in town too, and right before and during off-season periods, you'll get nice prices looking for "rooms to let" signs. Average per an apartment is 20 euros/night.
You can spend time at the marvellous beaches, even partying there at night. It is also at night that most shops open and the town is alive (at least during the summer).