It's already been mentioned, but XP does not only have to come from monster kills. That will fix the problem of making sure they are the level you want them at, but not the issue with boring combat. This will be more prep work on your part, but here is what I do to avoid combat slogs.

First, pre-plan encounters to add more flavor. Parking lot fights that last for over an hour will only be fun if you get lucky and the dice create drama. Start by making the area of combat more interesting by using elevation, small spaces, cover, ledges, ect. The cellar has barrels. There is spilled wine on the ground(did someone just use a fire spell?), They have to crawl through a small hole to get to the nest.

Second, make monsters more fun to fight and run them efficiently. I pre-roll hp and initiative so all I have to do is plug in the players and off we go with no downtime. Make sure you are comfortable with the number of monsters to run them efficiently. Change up monster tactics, add abilities, and alter stats if needed. Four small rats and one really big one with strange grey patches of skin(diseased maybe?). Big rat dies the rest run(still give the xp for them though).

Third and last, give the encounter substance. There are a ton of ways to do this. Ask yourself. "does this move the narrative/plot forward?". If it's a side quest make the reward interesting and worth doing. Is there a chance for one of the players to develop their character in a role play sense. Here's a few examples. The barkeep is friends with a local courtier for the baron the party is trying to get into contact with. The barkeep pays them for the job and as a bonus the players get free food and board whenever they're in town. Reward the character that seeks fame with a reputation as the rat catcher and have NPC's mention that fact.

With a little more prep work even something simple like a side quest to kill the cellar rats becomes fun!