I used a lot of taxis for intercity trips in Albania when the buses were not convenient, but I imagine I paid over the odds on some occasions by doing that. I'm not sure I ever saw a real bus station in Albania, just parking lots. In Tirana there were different departure points for different destination, and they sometimes seemed to relocate. Online information wasn't always reliable. Those bus lots are not necessarily convenient to the historic center, but there should be taxis readily available.
Berat is a good choice, I think. I took a bus there. I don't remember the duration of the ride, but my notes say 2 to 3 hours. In case it's helpful, I'm listing my Berat sightseeing targets below; the list was compiled in 2022-2023. I didn't have time for all of them. Berat's hilly, so it takes more time to get from place to place than would be the case in Tirana, for example.
There may be a city walking tour, but likely requiring a certain minimum number of participants.
Berat Castle, Rruga Mihal Komnena: 13C fortress (country’s best) where people still live, shop and dine. Gardens. Spectacular views from parapets, but tough uphill walk. Has multiple handsome orthodox churches; should be possible to find someone to open at least one of them. Go early to avoid crowds. Need exact change for ticket (200L 2022).
Shen Todri (St. Theodore’s): Frescoes.
Onufre Museum, Kisha Fjetja e Shen Merise (Church of the Dormition of St Mary): Albania's finest collection of icons inside 18C cathedral, largest church in Kalaja neighborhood. Don’t miss chapel behind iconostasis or its faded, painted cupola. Enchanting church if no tour groups are present. Ask here whether can see the other churches in this district, which are normally locked.
Shen Meri Vllaherna (Chapel of St Mary Blachernae): Rebuilt 1578.
Kisha e Shen Kollit (St. Nicholas)
Kisha Shen Triades (Holy Trinity Church): Off side of Castle Hill. Substantial and picturesque.
Red Mosque: First in Berat (15C). Near SW wall of fortress.
St. Demetrius Church, E end of Bulevardi Republika: 16C frescoes among best Byz art in Albania. Building reconstructed 1929. Not far from Old Town.
Muzeu Etnografik (Ethnographic Museum): Excellent museum in beautiful 17C/18C Ottoman house (as much of an attraction as the exhibits. Info sheets in English. Just off hillside leading up to castle.
Solomoni Museum, Rruga Mihal Komneno: Jewish Museum. Takes about 30 minutes.
Xhamia e Mbretit (Sultan’s/King’s Mosque): Beautiful ceiling. One of Albania’s oldest mosques. Can see inside immediately after prayer time.
Mangalem Quarter (Old Town): Old Muslim quarter.
Xhamia e Beqarevet (Bachelors’ Mosque), Rruga Antipatrea: 1827. Porches and interiors covered in dizzying array of brightly-painted flowers, fruits, leaves, swirls and arabesques. Fine Ottoman-era shopfronts nearby. Down near river.
Gorica Quarter: Old Christian quarter, with churches. Quieter than Mangalem Quarter. Top of hill.
Gorica Bridge: 18C Ottoman stone bridge.
Xhamia e Plumbit (Leaden Mosque), Rruga Gaqi Gjika/Rruga Antipatrea: 16C
Bulevardi Republika: Xhiro (passeggiata).
Rafting Trips: www.albrafting.com
Tourist office: http://bashkiaberat.gov.al/
Albania has the most cash-oriented economy I've seen. Smaller hotels may want cash. Some non-touristy restaurants want cash. The only time I used a credit card for transportation was on the bus from the airport to Tirana. ATMs have very high fees. Money-exchange booths are often cheaper. Euros preferred but US dollars may work.
Take a scarf to cover your hair and wear conservative clothing (long sleeves, knees covered, etc., in mosques and Orthodox churches. I've run into a lot of Orthodox churches that do not allow photography, but I don't remember whether some were in Albania.