I made vice admiral the other week, and now I'm not sure what it is I should be doing now. I see a lot of vice admirals playing, so I know there's probably lots of stuff to do, so I'm curious what sorts of things should I start doing now?

Please keep this constructive. "Quit the game and get a life" comments aren't really that helpful.

Have you finished all the episic missions yet? Chances are you haven't.

Then there are all sorts of dailies, PvE queue missions and events, PvP, STFs, building a Starbase with your fleet, the new reputation progression system, Foundry missions...

Most people will say STFS
I say relax take a couple of days off then get back to whatever you most enjoy (in my case missions)

Foundry missions, can be found under the foundry tab in the missions window.

Strike Forces can be found under the PVE queue button on your hud.

Have you been to Defera and done the Defera invasion zone?

There is also the Romulan Adventure Zone on New Romulus.

You then also have PvP if you are interested in that.

Join a fleet and help build a fleet starbase.

All of these offer various rewards, marks, equipment, EC, etc.... You can then use this to improve your ground equipment and ship equipment.

Check out STOwiki.org for more.

A) Whatever you want.

I went through and redid all the missions on Elite. That was fun.

collect pretty rocks and tag Epohhs, wander aimlessly across a gorgeous map doing quests suited for the opening starter zone of a cheap fantasy 1-year-wonder MMO, and...oh, yeah, buy dilithium with lots of zen to feed the rep grind.

I got stuck on one Romulan mission. Every time I tried to do it, the warbird would seriously destroy me. Finally just gave up on it.

I've been doing a lot of Starbase 24 as it's enjoyable. And I kind of fell into doing Mirror Incursion whenever it pops up on the hourly list.

I'd like to help build our fleet's starbase, but I understand that takes DL, and I am seriously lacking in the gathering of that sort of stuff.

The problem I've had is I just don't know where to start anything, or what to start, so keep doing the same missions over and over again. I went to Q's Winter Wonderland yesterday and wandered around before I couldn't figure out how to do anything interesting.

Spend some time figuring out what content is actually available to play (the wiki has a list of daily missions which pay dil).

Try some doffing.

Trade stuff on the exchange.

Learn about the game mechanics and improve your ship build - the levelling process really doesn't teach you anything about this, and the in-game descriptions can be a bit misleading.

Play the content you enjoy playing.

Right now you can get the Breen ship from Q's winter wonderland and some cool stuff from featured episode replay - so maybe prioritise those activities if you like free stuff.

Depends entirely on what you are into I'd say.

Albeit for the moment you need to check out the christmas event and specifically the free ship where you have to do a daily 25 times to get it.

What I did was ignore everything and race to level 50 knowing the rewards were better.
Then I jumped straight to elite stf's again because of the rewards.

I never read a single textbox or spent time on anything but going for max profit.

However now stf rewards are locked out I'd probably pick items from episode runs especially ship items like deflectors etc. for my build.
Possibly also even ship weapons depending on the kind of time and willpower I had. If not simply find some cheap second hand weapons on the exchange.

I don't know if I'd even do reputation or stf on a new character. I have a fresh alt and i have yet to bring him into stf or a romulan mission because he doesn't have neither the exp or the EC's for it.

Whatever you are into though I strongly recommend you start doing doff'ing as your no. 1.

They take time but it's passive time so you "level up" while you are afk or doing other stuff.
Doff will earn you EC's, items and new or stronger abilities for your boff and overall build.
You should go for colonization, confiscate contraband, console fabrication and officer exchanges.
There is like a top 5 doff assignments you have to do daily because everyday you aren't doing them you are losing profit

It is kind of funny, and your question isn't atypical. You have managed to play through the game, hit the level cap, and by your own admittance, don't have a clue how to do anything. My suggestion is to stop playing those overly easy episodes and learn how to play.

You need to learn how to Doff, get dilithium, get fleet marks, get omega marks, get romulan marks, build a ship that doesn't blow up at the site of a romulan warbird.. which is bad. Then there all kinds of fleet actions, reputation unlocks and equipment to earn.

The levelling process needs to change, by allowing players to bury their heads in episodes they get too much of a shock when level 50 hits.. the episodes reward nothing of real value to the end game.