Plugshare is a great resource for finding Tesla (Superchargers and Destination Chargers) and non-Tesla chargers - and something I'll usually check before going on a road trip to identify alternative charging options, in case a Tesla charger is unavailable when we arrive.
The interior cabin A/C will likely run only if you have overheat protection enabled - otherwise the interior will get hot (which is the likely cause for the console touchscreen discoloration/bubbling problems). If you're parking all day, a windshield sunshade may have minimal impact on interior temperature, primarily shielding the area underneath from extended UV radiation.
The battery pack cooling/heating system will likely run periodically to keep the pack within the operating temperature range.
For a 7 day cruise, with all of the power saving features enabled, you should be OK. After disabling overheat protection, the largest vampire draw is likely running the onboard processor (which happens if you have Always Connected enabled or if you are using Sentry mode).
I always have some anxiety about leaving our Tesla parked at the airport or cruise terminal for cruises. And sometimes will do a 12 hour or 24 hour parking measurement prior to a trip just to restore confidence we'll have sufficient charge when we return.
If you're going to the Galveston cruise terminal, we've parked our Tesla at the port several times for 7 day cruises - and haven't had a problem.
Stopping at one of the west Houston superchargers on your way to the cruise terminal, and getting nearly a 100% charge would give you the maximum charge when you park. The best supercharger would likely be at Rudy's at the Grand Parkway and 59 south of Sugar Land. You can get a full charge there and then drive highway 6 to Galveston (usually missing most of the traffic). Though you could also use the Supercharger on 290 near Beltway 8, but that will require driving cross town and down the Gulf Freeway where you might encounter more traffic.
There are also multiple
destination chargers in Galveston.
Port Parking and
EZCruiseParking have Tesla and generic chargers, including car covers to reduce heat when parked outside and some indoor parking spaces. Plus, Moody Gardens has a couple of Tesla chargers, in case you need to add enough charge to make it to the nearest Supercharger.
As long you enable the power saving features (do a test park at home to estimate daily vampire drain), you should be fine. We've made multiple trips parking at the Galveston cruise terminal for 7 days and last year parking in a Houston airport garage for a 14 day trip - and we've been fine (though we usually charge to near 100% before leaving home, just to give us a little more cushion).
