While true that the 2960 is not a full Layer 3 switch, a 2960 does support inter-VLAN routing using up to 16 static routes (need to update IOS to LAN BASE and at least the version below). Routing protocols aren't supported though so no EIGRP, OSPF, BGP, RIP, etc.
Instructions here:
A larger environment would be better off with a layer 3 switch but a small environment should be able to get by with the 2960.