Torshavn basically has two hotels in the center of Torshavn and three on the outskirts. The two newest hotels are on the outskirts. These three hotels have the best parking.
Honestly, I would just set up camp at one of the Torshavn area hotels and take day trips. The Faroes are not that big and most of the islands are connected by tunnels. Driving from Torshavn to the furthest point not needing a ferry is one hour. And if you do need a ferry, most leave from Torshavn.
Make sure you understand the driving rules in the Faroes:
https://guidetofaroeislands.fo/travel-information/driving-in-faroe-islands/
You'll find that getting to the Faroes is not as easy as you think. Flights from most locations are not every day except for Copenhagen. Additionally, July is prime tourist season. The hotels will fill up. Make reservations early.
I stayed at the Hotel Hafnia in 2016. Since then it has been renovated. However, parking is limited to street parking with a limit of 8 hours. The Hilton Garden Inn on the other hand offers free parking on site.
Also be aware that buses in Torshaven are free.
You say you have been watching youtube videos but the Faroes have some excellent tourism websites:
https://visitfaroeislands.com/en
https://visittorshavn.fo/