In Paris, buy a bottle of wine, some cheese and a baguette and head to Sacre Coeur right before sunset.
Find a spot on the stairs leading up to the cathedral where you can see the Eiffel Tower.
Sit down, pour yourself some wine, snack on cheese and bread and watch the sun set over the city and the lights come on at the Eiffel Tower.
Always been one of my favorite spots to take people.
The view is a bit better from the dome of the cathedral, but they charge you 6 Euros or so to climb the stairs ;)
There's a walking tour of the catacombs, it's been ages since I have done it. The entrance is near the Denfert Rocherau Metro.
Don't remember how much it was. But I am sure you can find it by googling.
It's a bit creepy though. You'll see lots of skulls and bones.
One of my favourite ones used to be a (cheap) coffee on the rooftop coffeshop of the Samaritaine department store, but unfortunately that one has been closed for many years now. There's always rumors about a renovation, but not much seems to be happening.
Cologne has a lot of attractions concentrated right around the Main train station (the cathedral is there, you can walk through the Altstadt and find one of those Brauhauses that have been mentioned), there's a bunch of Museums in that area too.
If you have it in the budget river sightseeing tours are fun in both cities Paris and Cologne, but they are $$$
You can do a harbor cruise in Cologne too, which is quite fun!
Both cities are really great to walk around in, take public transportation and just get lost and go with the flow, if you like that way of travelling...
Have fun!! Sounds like you are planning an awesome trip!
Edit to add: An awesome spot in Cologne are the Rheinterassen
You'll have a great view of the city, there's even a beach, where you can chill and have a Koelsch
Food is a bit $$, but decent quality
It's a spot you will enjoy any time of the day, at night when the cathedral is lit it's spectacular, but
it's also awesome during the day, with the boats floating by and the view of the city.