[I am not a lawyer. If this post raises questions for you, seek legal expertise locally.]
If there is to be a club, then it has to have a place to meet, preferably without having to pay a fee.
If I were in a new town and wanted to start a group, the
First place I'd try would be the local library. Libraries have always been supportive of small arts organizations. And that's what a ukulele club is--a small arts organization.
Second is a religious or community center. Churches often have community rooms that they make available to local organization.
Third is a bar, sandwich shop, or any other place with a public performance license. Any business that regularly offers music is a good bet. However, be considerate. A business may be eager to support music groups, but if it doesn't know about license requirements, it may get a visit from ASCAP or BMI resulting in a fine, and threat of a lawsuit if the fine is not paid. If you do find a business that will host the meeting, it's a good idea to support them by ordering food items before, during, or after the meeting.
Public performance licenses are one reason why libraries and churches are excellent places to hold meetings. A club meeting that is not open to the general public is not a public performance.
Important! NEVER run over your allotted time, especially when the space is being provided by a business. Be sure the room is returned to the condition in which you found it and everyone is OUT THE DOOR by the time of the meeting's scheduled end. A good rule is to never start a song within 15 minutes of the end of a meeting. This allows plenty of time for conversation, stacking chairs, and doing whatever else is necessary to restore the room to order. Nothing builds up resentment faster than keeping staff past the time they are being paid to work.