Most of my advice is probably similar to Macharius, but here you go.

If you will be commuting during off peak times, then the 20-30 minute limit would give you quite a range from the UofM. If you are looking at commuting during rush hour, then your options are more limited. The University is very central and many routes to get there will run into other traffic headed to Downtown Minneapolis.

Roseville as Macharius mentioned would be a good option. Some other northern suburbs might work too, but personally I wouldn't recommend Columbia Heights. Around here, is is sometimes referred to as "Cocaine Heights". Fridley to the north of there might be fine, but you might be pushing the commute. I'm not certain.

Personally, I prefer the southern suburbs better. It might just be familiarity, but they have a reputation for having more to do. Richfield and Bloomington would both have a decent commute. Parts of Eagan as well, but you will need to look at different Highway access options from there.

Parts of South Minneapolis and the Western side of St Paul would give you an easy commute and have a relatively suburban feel compared to larger cities. The housing stock is older on average, but often well maintained.

Edina Realty is a good local realty group if you are looking to buy. I bought with them and could recommend a realtor if you want.

Welcome to the area.

If you have more specific questions about any particular areas or considerations (shopping, politics, demographics, etc) I can try to help.