There should be no tax considerations and it's very common to leave and re-enter for a new visa (Mexico at least)
You have to have an auto permit so have all your papers ready for that. You don't say how long the whole trip let alone how long you'll stay in each area. Apartment rentals are hard to find for short periods so will probably be stuck with motels/hotels.
Internet access is pretty good in most of Mexico but you'll be limited to Internet Cafes of which there are many
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