If I had a vote, it would be for orbiting a planet. Most episodes had the ship orbiting the planet of the week, and even the intro had shots in / leaving orbit. I also think it would be cool to hop in a shuttle and fly down to the planet and/or beam down... but that’s a whole other ball of wax.
Which is why I’m tempted to do Starbase 11. Here's what would be an brief flow of the ideal experience:
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1. Start off as Admiral or Commodore aboard the orbital drydock office facility
2. The Enterprise arrives for resupply and inspection. You watch out the facility's lounge viewports as she drops out of warp and approaches drydock.
3. Go to the drydock office's hangar bay and board a shuttle
4. A pilot takes you on an inspection tour of the Enterprise, starting with a cruise around the vessel's exterior.
5. The shuttle swings around after the exterior tour and the shuttlebay doors open as the pilot guides the vessel in for a landing
6. Shuttle lands, you disembark, and are greated by Kirk, Spock, and McCoy, as they proceed to take you on a tour of their vessel. Your shuttle leaves you in their company as it returns to the drydock facilities.
7. Take tour of vessel, exploring the Enterprise at your leisure, bumping into various characters from the series, finding Easter Eggs, reading data slates, etc.
8. As your tour concludes in the transporter room, beam down with the senior officers and proceed to M-11 Starbase Club for drinks and chat with the young, but respected Captain of the Enterprise.
Okay, okay. A lot of that "running into the characters from the show" would be extremely difficult to do without a full team of professional animators, voice actors, etc behind me. So we may have to find a way around that

But a guy can dream, eh?