Samsung Galaxy Nexus has a 16GB internal memory and no external sdcard. I'm wondering if that means I have 16GB (or at least the free space left of that memory) to install applications?
Yes you have full 16GB for apps+data together in a single file system. You won't have to do any moving to SD card any more.
To make it more generic:
By the way: This is the reason why there's no USB-thumbdrive functionality any more for the Galaxy Nexus (because /sdcard is not a single partition any more and also there's no FAT32 formatted partition internally (except for SD cards if existent))