1. A system, comprising: a virtual compute instance, wherein a virtual graphics processing unit (GPU) is attached to the virtual compute instance, wherein the virtual compute instance is implemented using central processing unit (CPU) resources and memory resources of a physical compute instance, wherein the virtual GPU is implemented using a physical GPU accessible to the physical compute instance over a network, wherein the virtual compute instance is provided by a multi-tenant provider network, and wherein the multi-tenant provider network comprises a plurality of instance locations for physical compute instances and a plurality of GPU locations for physical GPUs; and one or more computing devices configured to implement an elastic graphics service, wherein the elastic graphics service is configured to: select, in the multi-tenant provider network, a GPU location for the physical GPU or an instance location for the physical compute instance based at least in part on one or more placement criteria for optimization of placement, wherein the placement criteria are associated with use of the physical GPU by the physical compute instance; and cause the physical GPU to be provisioned in the GPU location or the physical compute instance to be provisioned in the instance location; and wherein the virtual compute instance is configured to: execute an application using the virtual GPU.