I was just thinking up some possible missions Cryptic (hi Gozer!) or someone using The Foundry could create in the future (might work as beginning missions for future episodes, too) that would be entertaining and different from what we already have in the game. Here are a few ideas. I realize these are far from polished and may not be immediately feasible, but they might be ideas for something in the not so distant future that could probably be done.
A ship that went missing years ago is found intact (possibly damaged) and adrift, broadcasting a distress signal. When the player is in the vicinity, something could pop-up to offer them the quest. Upon entering the system, the player's ship attempts to hail the other ship, but receives no response. A sensor scan reveals minimal life support is functioning and artificial gravity is still functioning. Life sign scans are inconclusive (possibly due to radiation or some kind of anomaly within the ship). An away team beams over to investigate. They discover the distress signal was automated but hasn't been picked up until now due to interference from the system's star, which has some kind of special properties that interfere with subspace communications at close range. Gravitational pull from a comet or some other spatial body slowly dragged the ship far enough away from the star, that eventually the signal was able to get out just recently. The away team's objectives are: search for any survivors and/or to get conclusive life sign scans, access the ship's computer to gather logs in an attempt to find out what happened, create a data link back to the player's ship and upload the logs, determine what if anything is salvageable (perhaps it has some useful dilithium crystals still or something like that), and then to beam out. Another spin on this, perhaps a contagion was beamed aboard after an away team mission, which eventually killed the crew and the ship had been adrift ever since, until it got caught in the gravitational forces in the system and ended up where it is now. The player's away team may even inadvertently return to their own ship with the contagion, and have to quarantine those carrying it, or develop a cure in Sickbay (sort of like in the Memory Alpha / K-7 mission) to save the crew from the same fate as the other ship's crew. This could offer a non-combat, non-diplomacy mission that is just investigation-based, perhaps with one or two puzzles to solve to open up sealed doors or access computer data, etc. Or re-routing power to bring certain things online so they can be used or accessed (computer core, transporter, etc.)
An ambush mission - mostly played out inside the player's ship. Your ship is in orbit of an unexplored planet, which perhaps used to be home to an extinct civilization. Maybe the player has an away team on the surface excavating ancient ruins or conducting a survey for possible colonization. The player captain is aboard their ship, when an enemy ship suddenly shows up (or decloaks perhaps), attacks without provocation, deals significant damage to the player's ship, and beams over several armed boarding parties to key locations (engineering, sickbay, the transporter room, etc.) and seizes control of the player's ship. The player and some of their officers actually battle in the corridors and in the different areas throughout the ship, killing or incapacitating the invaders and gradually recapture the ship and re-exert control over it. Each area freed counts as an objective met (for instance 1/5, 2/5, 3/5, etc.). At the end of all this, a brief space battle would ensue, and perhaps end prematurely with the arrival of Starfleet reinforcements destroying or driving off the hostile force. The enemies could be some kind of unknown aliens, Romulans, mercenaries, or whoever. In all the Trek series, we've seen scenarios where enemy forces captured Federation ships and the crews had to outfit or fight them. This would be one of those kind of missions. You may recall examples such as the Ferengi capturing the Enterprise D (TNG: Rascals), the Jem'hadar capturing the USS Defiant (DS9: One Little Ship), the Hirogen capturing the USS Voyager (VOY: "The Killing Game"), the Kelvans hijacking of the USS Enterprise (TOS: By Any Other Name), Sybok hijacking the USS Enterprise A (ST V: The Final Frontier). In my opinion, a mission like this would be classic "Trek" like and potentially very fun. I think it would be even more fun if player could form groups to do this sort of a mission together with a friend.
Another mission involving the Guardian of Forever could be very fun if well written and designed. It would need to be something completely different than Past Imperfect or the TOS episode featuring the GoF as to be original, believable and fun to play. One idea I did "conjure up" was maybe a Federation archaeologist discovers a planet that was home to a race which has long since disappeared or gone extinct, and sends a small team back to observe them or to investigate what wiped them out, with the intention of observing only, and then some kind of trouble ensues and they have to get back without disrupting the timeline, which might lead to some painful choices having to be made (not interfering but seeing others in pain). I'm wary of another time travel story at this point since there have already been a few, but... some of them have been among the most fun of all the missions so far, too. If it was good enough and believable, it might work.
We haven't had a Prime Directive related story or crisis yet as far as I'm aware. It seems fitting that we should at some point. Perhaps with an accolade (or two) achievable depending on the choices the player makes. The mission would be replayable so that they could obtain both by taking a different path the second time around and getting both accolades. This could be a pre-warp civilization mission of some kind, or a negotiation for certain rare and valuable energy sources / minerals or medicines which can't be replicated that are produced from herbs that won't grow anywhere else but on that planet, or something along those lines. In the course of the mission, the player would be presented with certain choices, and depending on the choices, a couple of different outcomes would happen. Do they let some injustice stand due to adherence to the Prime Directive, or do they choose to interfere? They would have to weight the pros and cons of each decision along the way, and depending on that, the story would unfold a certain way or another way. This quest would also give diplomatic XP and perhaps some kind of special reward.
These are just some ideas but I did spend a lot of time thinking them up and trying to come up with some good ones. I hope you like them. I know they aren't perfect, please be kind. lol