Three nights is plenty for Cartagena. Two full days is ample. Three days at a stretch
Not only is there not much to do around Cartagena for 70 year olds but save for enjoying the ambience of the city there is not much to do for anyone at all.
They can go along the coast to Santa Marta and stay somewhere with nice beaches for a few nights then fly SMR to BOG to go home. Accommodation is getting tricky to pin down but I happen to know Hotel Aité has a double room with partial sea view from 4-9 January so worth looking at an option like that.
Bogotá has a tropical mountain climate so Bogotá does not care that it is January. It is not going to be cold. I like Bogotá in the first year of the year, fewer people around and less pollution. Normally it is sunny and blue skies but this is not predictable. Last year it was only sunny on Boxing Day and rained like crazy until about May
If your parents are into history then you can maybe consider a side trip to Mompox from Cartagena.
Have a great trip and definitely go to El Baron and Alquímico to get mashed up on fruity cocktails. Also Epoca is a godsend in the blistering heat. It's a tiny chain of two coffee shops that have air conditioning and light lunches. Worth pinning them to your map before you leave as you are definitely going to want somewhere to go to sit down and cool off a bit.