Currently the daily quests are fairly simple and with the exception of the toads, don't really require anything special on behalf of the player (no questing needed). Play just about anywhere for a little bit and you'll kill anyone you need to. Have you considered having other quests added to the list to encourage different play styles or areas? One of the benefits of the current system is that they can be accomplished by anyone and are not difficult. Some of the options I list below would need to have some filtering to determine whether a player could get them (can't have Heroic quests assigned to someone whose highest hero is level 15, can't assign a Mage quest to someone who doesn't have any Mages, etc), and you wouldn't want a quest that is so difficult or time-consuming to complete that it becomes frustrating, but adding a little variety into the quests might give them a little flavor. Others may prefer them as they are, especially if they are locked into a specific game style (like high-level Trial farming). You would also need to determine whether quests should be filtered based on the account as a whole or on the hero getting the quest (heroes at level 9 for quest farming can or can't get quests for high-level requirements or for a different class).
- More variety of monsters from higher-level areas (dragons, mechs, etc)
- Gain 1 Story-mode star (not given to players who have already earned all stars)
- Beat 5 Trial bosses (can be the same boss repeatedly) (should be doable by any player with trials unlocked)
- Repeat an accomplished Achievement (would be limited to Achievements already accomplished, and maybe limit to the easier ones to complete)
- Beat TBD, TT, and CM on XX difficulty (highest difficulty the character has beaten)
- Gain 5 gemstones
- Deal XX damage with skill YY (would need to be scaled for the player's capabilities)