Your existing 3750G is a L3 switch. You could either just define new VLANs at the port level on the 3750G and/or extend some VLANs to downstream connected switches via VLAN trunks. All the inter-VLAN routing could then be done on the 3750G. You could also preserve addessing for some of your servers, although if then are located off different switches, it will make keeping them on the same VLAN a little more complex.
The 4507R is a nice device, although for your size network, a stack of 3750s might suffice too. For either device, you could bring all VLANs to it, and again route all your subnets on it, or use the existing 3750G and new 3560s as routers. In that case, you would might have different subnets, in the same VLAN number, but not the same VLAN, off different L3 switches.
Further, on the new 3560s, your new diagram shows them as being used as L2 switches, so unclear why you don't obtain L2 switches instead.
BTW: in locations where the network devices are in the same room, you might want to consider 3750 or [new] 2975 stacks.
PS:
From the name of the device locations, and your choice of the 4507R, redundancy might be very important. If it is, you might want to especially consider that stackable switches and multiple links between different or redundant devices.
