How much time in Aarhus?

I'll give you some things to see/do, then you can pick what you like and sum them up to a number of days.

Absolutely first priority for us every time we're in Aarhus is Den Gamle By. An open air museum of old buildings from 1864 - 2014 (yes 2014 is now "old time"). We ususally spend an entire day there. Having lunch in one of the restaurants.

Lighthouse - Highest building in Aarhus with a fantastic view of the city and the bay. Sea life museum in the basement.

Aros - Art museum. We are not really into art, but the rainbow walk on top and the little boy are amazing.

Salling roof top garden - including bridge with glass floor over the pedestrian street. (Sorry, I couldn't find an English version, but the pictures say it all)

Hotel: If you are driving I recommend Scandic City. Entrance to the parking is from "Hans Hartvig Seedorff Stræde" no 1. If you go by public transport, you might want something closer to the station.

Eating:

Visit "Åboulevarden" - a long row of restaurants/bars/cafes along the old city stream.

Aarhus Street Food Market. Best for lunch. Too crowded for dinner - at least we have never been able to find a seat.

Great tips already by enersen.

If you have a car and like old tall ships I recommend to take the turbo ferry from Sealand (Sjællands Odde) to Ebeltoft and visit Fregatten Jylland. On the way to Aarhus you can visit Rosenholm Castle.

In Aarhus I find the architecture of Aarhus Havn area is partly remarkable. The art sculpture Sea Pink is a great chance to see the world a little bit more in pink.

When I traveled through I slept at Zleep Hotel Aarhus Viby which was acceptable for a good price. I disliked the Cabinn Hotel Aarhus at a one night stay.

These are great tips! Thanks!

Do you think we'd need two full days?

Of course this depends on how much you want to see and do. Aarhus and surrounding are definitely worth two full days.