"not only locally" is correct and usable in written English.
You can use this phrase to emphasize something that happens beyond the scope of the local area. For example, "This band is popular not only locally, but across the entire country."
Poulsen said: "The IPO will raise the profile of the company, not only locally but globally.
Over time he attracted a following, not only locally but also from out of town.
"It will allow for a lot more collaboration in learning, through Intranet activities and through the Internet, not only locally but around the world," she said.
The de facto local partners were state-sponsored organisations that support the double genocide model, not only locally, but in international organisations.
Those seats were among those considered important not only locally, but also as part of the Democratic strategy to gain control of the Senate.
A tape of this first performance of "Harmonium" began making the rounds, not only locally but even as far away as Europe.
Good programs — the Carr Foundation's Gorongosa Restoration Project in Mozambique, Island Conservation's re-wilding of islands in the Pacific and the Caribbean, WildEarth Guardians' fight to save the sagelands of the American West, EuroNatur's blending of cultural and biological conservation in southeastern Europe, to name a few — not only act locally but, by necessity, think locally as well.
The result not only works locally but sits comfortably next to the dollar and euro symbols.
Riometer absorption, on the other hand, is not only measured locally, but is available for exactly the same time slots in which the electron densities are measured.
However, the stem cell concept is changing rapidly as evidence is mounting that adult stem cells not only reside locally in specific niches, but may also be recruited from the circulation to actively participate in the regeneration of various tissues.
This labeled nanofibrous membrane function as a novel radio-medical appliance with excellent surface hydrophilic and mechanical properties that can be directly implanted into the lesions not only to locally kill the cancerous cells but also to play the anti-adhesion role at where surgical procedures have been made to remove the tumor tissue.
