Hi Chococake,
What would be your purpose at the neighbouring university? I had an arrangement with my local university to have access to the library and communal computer facilities as I was 5 hours drive from my university. My supervisor arranged with my university library to endorse me as a student which then provided me with a Sconul access card to use the local university facilities. Both universities were part of the sconul system which is designed to allow reciprocal sharing of resources. Not sure if this is what you are after....? If it is, then your library may be able to help in the first instance.