It is pretty easy to get to Lidköping, make sure to fly to Landvetter Airport in Gothenburg, Sweden. From the Airport you take the bus or taxi to Gothenburg central station, approximately 30min traveling distance. From Gothenburg central station you take the train to Lidköping, approximately 1h 45min traveling distance.
Arriving in Lidköping you find Spookyfish at a 5min walking distance from the station, almost everything in Lidköping is within walking distance so it is easy to choose your living.
There is a buch of options where to live, from hotel to hostel or even apartments to rent. We recommend you to check out https://www.booking.com
since most of the options you have is listed there. Just make sure to book your living within walking distance from centrum in order to make your stay as easy as possible.
WHAT ELSE IS THERE TO DO?
Of course you'll be busy with getting tattooed but since you have been traveling it would probably be nice to se a part of Sweden while visiting.
Check out Lidköpings own tourist guide (not the best but ok):
("välj språk" means "choose language" which can be har to find a the page)
For you traveling in the summer a nice activity is just to rent a car and experience the Swedish nature, Sweden have a unique law that allows you to be in the wild anywhere you like and you are allowed to camp anywhere for 1 day (except in someones garden or public spaces). And Lidköping has some beautiful nature with Kinnekulle and Vänern just around the corner.