please note that i dont have a partner but lots of these ideas are things i have done for others in my life or are ideas i have seen elsewhere. also most of these ideas work really good combined with some of the others
also lots of these can also be used for a parent, friend, sibling, etc
also people other than op can use these ideas of course (have to clarify because if i dont the back of my brain will worry that people will think that they cant use them)
a few of these may cost a bit of money usually that is only if you dont already own some (or most) of the supplies to make that but once you get those supplies you can keep them for future special things (if its baking stuff though it might expire so that you might need to use up quicker) like christmas (if you celebrate christmas), an anniversary, their next birthday, or someone else close to you's birthday
something hand made and that relates to them.
if you can sew and have fabric (could even be from an old shirt), and sew something (i sewed a scrunchie for my mom this year for her birthday for an example)
if you have a dollarstore near you (doesnt matter the brand of dollar store) you can pick out a nice card there and get some of the fake gem stickers and fake flower stickers (the ones that look "fancy") you can make a $1-$2 card look like its a $5-$10 card. this one is a little costly cause you have to get the card and stickers. i have done this before and the card was $1-$1.50, i got 2 things of stickers (butterflies and flowers) each pack was $1.25 and i was doing two cards (though i think i had some left over and used them on a third one) so the cards each costed about $2.25-$2.75.
making a food they like or a desert they like (though this one can end up being costly if you dont have some of the ingredients)
a picnic at a park (if you have a good park nearby)
if your partner likes going for walks, find a nice trail near you and go for a walk together.
i have more ill add as a reply just so this comment isnt too long (it already is sort of too long [in my brain] but i dont want it to be longer)
more ideas: clean the house (or apartment, condo, or where ever you live) or part of it
make them "breakfast in bed" or something like that
find some cool free attractions and take them there
(this one will require a bit of money but shouldnt be too much [unless you already have a blank cd]) get a blank cd (i have gotten them at a dollar store before) and make a cd filled with songs that they like and that remind you of them, take a piece of paper (can even be the one that comes with it meant to have the tracklist written on it) and decorate it (you can write the tracklist or do that on a separate piece of paper to give to them after they listen to it so the songs are a surprise the first listen). if you dont have a thing that can "burn" a cd or you dont have a cd player then a spotify (or any music streaming service) playlist will work.
a movie night at home. maybe if you can take them to a store before and let them pick out a snack or two before and you can watch one or a few of their favorite movies.