With booking less than 2 weeks in advance, deeply discounted tickets will be scarce.
Although I usually not promote them, have a look into FR
out of NRN
Another budget idea would be to stay in Germany and use Deutsche Bahn. They have tickets available for unlimited travel, but excluding ICE and IC
"Quer durch Land" is a day-ticket for 42 € available for Monday thru Friday; the weekend's version of it is called "Schönes Wochenende" for 39 €.
If you restrict yourself to one of our states, like Northrhine-Westphalia in your case, day tickets get even cheaper.
But Deutsche Bahn also has "normal" discounted tickets available and also promotions for travel to other countries.
For destinations ...:
From Cologne take the slower (= regional) trains along the river Rhine upstream towards Koblenz (currently, national flower exhibition is being held there) and on to Frankfurt. Will make for a scenic trip.
As an A.netter you, of course, can opt to head for the airport in Frankfurt. But if you have no intention to visit FRA
nor Frankfurt itself, consider to turn already at some earlier city.
BTW, recommending anything, of course, would be easier for us if we would know about any special interest and no-go's of yours ...
Carpe diem ! Life is too short to waste your time ! Keep in mind, that today is the first day of the rest of your life !