Remote Desktop Connection without Internet
If you’re asking for a remote desktop solution that allows you to view/control your desktop/laptop from your Android mobile device over local wireless network, the answer is: Any RDP/VNC app.
Personally I use PocketCloud by Wyse. It supports both RDP (Microsoft Windows, built into the OS) and VNC (cross platform, if you have a Linux computer or Apple toy you want to view/control, or you prefer VNC on Windows) protocols.
Either RDP or VNC will work over a local network and, if you have proper firewall configuration and DNS setup, can be used over the public internet as well with reasonable security.
VNC requires a server to be running on the computer you wish to control. There are several “flavors” of VNC out there, and many of them are free (as in beer). Check out TightVNC for a pretty solid version.
RDP requires you to enable Remote Desktop on your computer. In later version of Windows it is disabled by default.
The good thing about both these tools is that they are protocols, not confined app systems. As in, you don’t need a Microsoft App on your Android tablet to view an RDP session, and you can install any VNC viewer app on your tablet/phone to view any type of VNC server. (Note: With certain types of authentication in VNC, I’ve found some viewer apps don’t work. Just find the right combination for what you need.)