You can change your business location pretty easily in your Thumbtack profile, by simply changing your address and travel settings. The nice thing about Thumbtack, is that the leads come right to you, even if you're new to the area - such a great way to get solid leads no matter where you go.
As far as moving a business goes - I have moved from Utah to Oregon and back to Utah... I hit social media really hard before moving and I also reached out to different possible business referrals to try and build my network ahead of time. In my case (I'm a wedding cake baker) I reached out to different venues, a school that offered baking classes, and a couple of wedding photographers in the area - and we ended up referring a lot of business back and forth.
You could reach out to health food/supplement stores, maybe some smaller gyms that might not have in house trainers (I know my local rec center let's outside trainers in), even to wedding planners who might have brides/grooms ask them about personal trainers to help them get in shape for their big day? I'm just brainstorming here - you can surely come up with better ideas than this cake maker (maybe I should hire you to help with the extra cake-making calorie intake??!)