What router do you have now? Are there items close by (microwave oven, cordless phone, baby monitor, fluorescent lighting, etc.) causing interference?
The all in one combo modem/routers given out as leases tend to have the weakest wifi signal/range. You'll get the best range using a stand alone router with 4 or more big ugly antenna like the Linksys WRT1900.
After you get done buying the new router AND figuring out how you will power the video camera without having a power outlet, you'll also want to place the router where it has a clear line of sight to the camera. That location may not give you good WiFi coverage throughout your apartment. Somebody not particularly memorable once said "Life is a series of compromises." Of course you could also complain about inadequate security to your building manager or homeowners association.