Yes, the Hilton is not a good choice as you don't have much free time.
It also makes your transfer to Ballerup longer ( sorry if I am harping on about this point...).
It will eat up too much of your time off.
If you were only going as a tourist it wouldn't be a big problem spending 20 minutes ( a little less with the normal trains ) going into town in the morning and 20 minutes again going back in the evening.