New Zoos that don't have the space or money for elephants, big cats, apes, or bears tend to focus on specific themes for their collections of small animals
Not sure I agree with this assessment. A lot of the zoos I've been to are smaller, and have very few (if any) of the species you've mentioned. However, with the exception of a few zoos that focus on native species, I've found most tend to have minimal theming overall, and oftentimes a rather random layout. For the small zoos I've visited:
Capron Park Zoo- no apparent theming
Buttonwood Park Zoo- formerly themed around solely native species, however more exotic species have been added in recent years
Elmwood Park Zoo- one section, Trail of the Jaguar, is a highly themed exhibit, the rest of the zoo has minimal to no theming.
The Wild Animal Park- no apparent theming, an unaccredited zoo with a collection heavy on cats.
Bergen County Zoo- primarily species from the Americas.
Prospect Park Zoo- no apparent theming, except for a focus on children's education and on smaller species
Central Park Zoo- split into three biome-based sections (Polar, Temperate, Tropic), plus a Children's Zoo
Queens Zoo- entirely species from the Americas.
Staten Island Zoo- no over-arching theme, however the main building is separated into themed "wings" (Reptiles, Africa, and Tropics)
Seneca Park Zoo- split into themed areas, each of which is focused on ABC species, with more megafauna than a zoo of its size probably should have: River's Edge (North American river otter, etc.), Cold Asia (snow leopard, Amur tiger, red panda, etc.), Rocky Coasts (polar bear, California sea lion, etc.), and Africa (Masai giraffe, African elephant, African lion, etc.)
Belize Zoo- entirely species native to Belize, many of whom are rescues.
Erie Zoo- some sections of the zoo have loose themes, namely the "Wild Asia" exhibit, but other parts are not themed.