Every US President has a statue in Rapid City. That's 43 statues, including one for the likes of Franklin Pierce (the greatest President of all time) and John Tyler (also a member of the Confederate Congress). Making statues for the sake of statues is and they're a great way of promoting a local city with a fictional tourist attraction.
So we have Kirk in Riverside, Iowa and now Janeway in Bloomington, Indiana. Logically, we should expand to the other Captains:
Picard: There are two La Barres in France, so they could race to build their own statue, although their population is in the low hundreds and this would be a poor attraction, having to be financed by outside interests and generating very little revenue. I don't know about the popularity of Star Trek (or just TNG) in Eastern France or if either La Barre is interested at all.
Sisko: New Orleans, and specifically the French Quarter, is an obvious locale for a statue or monument of some sort. But the city is so historic and influential, compared to all others on the list, that their may not be room for a fictional statue of a character vaguely connected to N'Orleans as opposed to the hundreds of known figures of the city who actually shaped the city. It would have to be small and built on private land (but where) and... well, there's a litany of issues here. Maybe a suburb with a fictional history of Sisko being raised there or something.
Archer: Upstate New York is a big place. Buffalo has statues of hometown Presidents Grover Cleveland and Chester Arthur in front of its city hall, so you can clearly imagine a more prominent Jonathan Archer inbetween them. More seriously, though, Archer's history in New York, even in non-canon sources, is vague and even the definition of "Upstate New York" is vague enough that any place North of Hyde Park can probably claim him if they want him. Outside of the new shows, Archer is probably the least likely Captain to get a statue. But I never thought Janeway would get memorialized, so who knows.
Other ideas:
Vulcan, Alberta - Has a statue of a Constitution class starship (the "FX6-1995-A") built in the style of the Enterprise-A, as well as an entire Trek-based tourist station (and annual Trek-themed conventions). Seems the obvious Earth-based locale for a statue of Spock. Other Vulcan-based characters, like Tuvok or Burnham or Sarek or even Surak, perhaps some day. But Spock is the most historically important.
Bozeman, Montana - there's been petitions and plans for a statue of Zefram Cochrane since it was mentioned in First Contact. Like Rapid City, there is no shortage of interest in statues in these Northern Rocky Mountain states, but a Cochrane statue ought to be very imposing if done right.
Going through the list of characters:
- McCoy - Atlanta, Georgia. Although he went to school at Ole Miss.
- Scott - Aberdeen, Scotland, per the show, although Linlithgow claims Scotty right now on a town plaque and other Scottish locales (Elgin, Glasgow) have sufficient cause to claim him as well.
- Uhura - Kitui, Kenya
- Sulu - San Francisco (although there's no shortage of Trek related stuff to be built in that city).
- Chekov - St. Petersburg, Russia.
- Pike - Mojave, California
- Chapel - Cleveland, Ohio
- Rand - Anywhere on Earth (probably North America) can claim her, although Grace Lee Whitney was from Ann Arbor, Michigan
- Riker - Valdez, Alaska
- La Forge - Mogadishu, Somalia (maybe not the best time to promote it, however)
- Worf - Minsk, Belarus (where he was raised, in some sources)
- Crusher - Clearly, just build a statue on the Moon. She's the most deserving.
- Bashir - Anywhere in Great Britain. Siddig was born in Sudan, but raised in London.
- O'Brien - Dublin, Ireland
- Chakotay - He's from outer space, but a Central American country (or Arizona) can claim his muddled ancestral heritage. Not sure they would want to.
- Paris - Portola, California. Or maybe New Zealand.
- Kim - Monterey, South Carolina
- Seven - Also born in Outer Space, but her parents may be from Sweden.
- Tucker - Panama City, Florida
- Reed - Anywhere in England. Dominic Keating is from Leicester.
- Sato - Kyoto, Japan
- Tyler - Seattle, Washington (kinda, sorta, not really)
- Stamets - Anywhere on Earth (probably North America). Anthony Rapp is from Joliet, Illinois, and the real world Paul Stamets is from Shelton, Washington.
- Tilly - Anywhere on Earth (probably North America). Mary Wiseman is from Gaithersburg, Maryland.
- Culber - Puerto Rico
- Lorca - Anywhere in the Southern United States (Texas, probably)
- Jurati - The character worked in Okinawa. Actress Alison Pill is from Toronto.
- Asha - Seattle, Washington (kinda, sorta, not really)
- Musiker - She was living by the Vasquez Rocks in California. Gabrielle Hurd is from New York City.
- Rios - Anywhere in Chile.