Repurposing very old hardware (Apple ][ era)

You could attempt to build a web server, that seems to be a very common project with very old systems. The third link I posted is a site hosted off one. You could also set up all your old favorite games to play. There are lots of resources out there of old computer projects.

Here are some resources to give you some ideas:

http://lostclassics.apple2.info/
http://a2gameserver.berlios.de/
http://servers.ld8.org/servers_apple2.html

If it were an Apple // GS I would suggest getting an SCSI or IDE interface card and putting proDOS AppleWorks GS and a couple of other applications on a hard drive. If you're into soldering you can build one. If it isn't a //gs, then you should back up all your floppies and use it only for games, like Eamon, or creating arty music videos.

As you've said you don't have an 80 column card, the 40 column text won't be all that well suited as either a (dumb) serial terminal nor as a way to work with AppleWorks 3. Perhaps you could use the original Killer App: VisiCalc.