In my opinion, Entwine is better due to the fact it has connotations of linking something and the meaning could be that the mayor and the town are entwined and the villagers etc.
However, the town name "embrace" indicates a love relationship and you may not necessarily live your town and in my opinion it sounds a bit cheesy but that's just me.
I like Entwine better because it reminds me of slowly knitting something. That something being your town and when it's finished it comes out as a beautiful town. At the end everything is linked to your town. That's just me though.