The real question is: Are they potentially entertaining to hang out with?
You don't seem in need of much of a social life, but I like to do stuff other than hanging around at home all the time.
Tell her you ain't a sugar daddy in a joking kinda way (hahahah or some emoticon), but if they want you can hang out at power plant mall for example, play some arcade games at Q Station, grab some cheap stuff at the food court.
Now she knows you are a reasonably normal guy and she may or may not be up for a movie / dinner at your place the next time.
If you think they're lame, dinner for two at your place, you're like the best german cook every totally
no space for big bro cause your apartment is too small, so sad