Adventures is the perfect expansion for Mission to exist in. Literally every mechanics-related theme gives you a reason to want extra turns in which you can't buy cards.
Events: As buying Events does not count as buying cards, if there is another Event on the table, often you will want to go on a Mission to get the coins for a $5+ event, or the coins and buys to buy an Event multiple times.
Reserve Cards: A Mission can be a great way to get your Reserve Cards into (or in the case of Wine Merchant, out of) your Tavern more quickly.
Duration Cards: Similar to Reserve Cards, you can devote Missions to getting Duration Cards into play to set up for a good future turn.
Tokens: You can use Missions to set up your tokens, whether that be upgrading cards with Teacher or Events, or flipping your Journey Token so it's ready to go for your next turn.
Travellers: Mission Provides extra cycling, enabling you to exchange your Travellers quicker, even on Mission turns. Also, many of the Travellers either attack or gain, so can be useful on Missions.
In fact, every single Adventures Kingdom Card can be directly useful on a Mission, either through being a Reserve Card, Duration Card or Traveller, using tokens, attacking, gaining or trashing/thinning, except Messenger, Port, Lost City and Storyteller, all of which can help with cycling and/or enable you to play your other cards.
In terms of Events, every other Event except for Borrow (unless you want a 4-card hand) and usually Travelling Fair, can be useful on a Mission, for gaining, trashing, setting up future turns, or setting up tokens.