Never used Ubuntu on an ARM processor, congrats! Does the Nexus 7 have the option of mounting without MTP? Haven't been able to connect my Galaxy Nexus phone to Ubuntu since Jelly Bean rolled out...
Mind you there are still a number of options. I know you don't want a cloud based service such as Ubuntu One or Dropbox, but that's probably still the best option if it's just a handful of files. Though still "over wifi", I'd recommend sharing a folder, drive or partition via Samba. It's not "on the cloud", it's on one of your machines. To enable sharing a folder outside your home directory, run
gksu gedit /etc/samba/smb.conf and then add
# Allow sharing of any partition
usershare owner only = False
Also you might need a password for Samba (even if you don't need it, it's a good idea). Run
sudo smbpasswd -a user (replace
user with your user name) and set a password.
Actually, full instructions here.