Is it correct to say “things are looking up for my travel plans” to indicate that I am ready to start planning my travel after so many problems.
In fact, for [person or situation with improved prospects] is by far the most common word to follow idiomatic things are looking up...
Presumably OP's doubts spring from the fact that usually the "subject" with "improved prospects" is a person (or at least, something "animate"). But that's like thinking there's something wrong with saying X is bad for my health rather than ...bad for me. Situations, plan, and other abstract nouns work just as well as people in such constructions.