• The first mission could involve going to a certain area of the map (say the gas stations), and picking up beer/cola or something.
• One of the missions might be racing Homer in Mr. Plow for a reward.
• Since Level 3 has the Duff Brewery, perhaps there could be a mission where Barney is employed or something, and helps collect Duff for the Brewery, but makes a mistake (drops it/loses it), and therefore isn't able to keep his job.
• Level 3 also includes the Krustylu Studio, so perhaps one of the missions could be working there. For this mission, you might need to purchase his uniform, like what he wears in Level 3 and Level 6 in the normal game, for a certain number of coins.
Those are all the ideas I have so far. If I have any other suggestions, I'll come back to you.