Will be in Copenhagen for a few days. Afterwards we have 7 nights to spend exploring outside of the city. Have thought about visiting Odense and Aarhus, possibly 3 nights in each. Not sure whether to rent a car, allowing us a little latitude to explore the countryside of those 2 cities, or just train and enjoy the freedom of being car free. It’s always a debate and having not visited Denmark before, we are unsure what to do. Any perspective would be appreciated.
Going to Odense and Aarhus and exploring the two towns you don't need a car. The train is much easier. Use https://www.dsb.dk/en/ to plan the trip and buy tickets. I prefer having a reserved seat, but it is probably not neccesary.
If you want to visit places outside the towns, check Google Maps or https://www.rejseplanen.dk/webapp/?language=en_EN to find out how difficult it is with public transport. In some cases it makes sense to rent a car for the trip.
Caveat: If you want to visit Odense Zoo (and I love zoos) Google and rejseplanen will only show you buses. I prefer https://www.aafart.dk/en/ - if you are there in the season.
Thank you for your thoughts. We probably need to better assess what we might like to do outside of those cities.
If you peruse Rick's book, he devotes a bit of time to the island of Aero, easily reached
by train from Odense to Svendborg (1 hour) and then a ferry boat to the island. I did
this, in the off-season for full disclosure, and it was a very nice contrast to being in the
cities.
In addition, to me Odense is worth a day or two (unless maybe you are a HC Andersen
fanatic).