For optimal performance, you want a direct connect between the server room L3 switch and each edge switch. (Basically, a classical star topology.) Whether you can support your edge switch distances depends on the kind of fiber and optics being used.
If your optics and fiber don't allow direct connections between each edge switch and the L3 switch, you could create one big ring, where you link each switch to two other switches, but the problem with that design, traffic now needs to hop though, possibly, multiple other switches. However, you might also have the option to create a partial mesh or some hierarchy topology. For example, perhaps you can directly connect locations 1, 2, 4 and 6 to the L3 switch, and location 3 to locations 1 or 2, and locations 5 and 7 to locations 4 or 6, so some other combination that minimizes switch hops.
BTW, if you only have a single L3 switch, that has no redundancy, it becomes a single point of failure for your whole network. If you have a stack pair, you can create dual Etherchannels links to the edge switches and perhaps to critical servers. Even without dual Etherchannel, with a stack pair, you can often preconfigure ports to be used if the other stack member's fails. I.e. downtime for such might only be the time need to repatch from the failed stack member to the still good stack member. (I.e. minutes of downtime vs. hours to days of downtime.)
