When reading about English Renaissance theatre, discussions centre on authors, theatre companies and theatre buildings in and around London. For example, the first English playhouses were the Red Lion, which opened 1567 just outside London, The Theatre, which opened in 1576, also just outside London, and the Curtain Theatre, which opened in 1577, also just outside London. Several other playhouses were constructed in the 1580s and 1590s, all just outside the City of London. (The London authorities didn't like playhouses. One reason was the influence of the puritans, who didn't like theatre in general. Another reason was that places where many people gathered together could facilitate the spread of diseases such as the Plague. Plague epidemics always led to the temporary closing of theatres.)
In all the books I have read about Shakespeare and his contemporaries, I have not found a single mention of permanent playhouses outside the London area. Theatre companies went on tour in England, especially when playhouses in London were closed because of the Plague, but it seems they performed in guildhalls and other buildings that normally did not serve as a playhouse. This leads me to the question where the first permanent playhouse outside London was constructed.
The article The Oldest Theatres in Britain mentions that Grand Theatre in Lancaster is "the third oldest theatre in England". However, I think this means that it is the third oldest surviving theatre; it is perfectly possible that other playhouses outside London were built before 1782 (the year in which the Grand Theatre opened) but that they just haven't survived.