Canebrake is much further out along Hwy 98 and has a golf course and lake, It has a variety of home types, including patio homes. Baywood has, as far as I know, the usual single-family type. Canebrake is one of the more prestigious areas in the city. It isn't for everyone.
If you are looking for diversity, the area around the university, neighborhoods in the University Heights section between 40th and Hwy 49 and Hardy and Hwy 11, generally speaking, offers that. (I would stay west of Hwy. 49) I live in that area (about a mile from Baywood Cove) and on my street we have Iranian, Arabic, Indian, black, and white families--professional and blue-collar--older and younger. It is in flux and whether it will be a gentrified area or slowly become more homogeneously blue-collar, I don't know.
The historical district near downtown is also something to check--offering restored homes and walkability. An exception to the west of 49 caveat.
Historic Hattiesburg Downtown Association
Innswood and Kirkwood are two neighborhoods off of Lincoln Road that are in town and have nice homes. There is a new area off 34th avenue that seems very upscale, but I know nothing about it.
Generally speaking, you are correct in assuming that more diversity will be found in town. The city has leash laws and other niceties (at least I like it)
while the Oak Grove area has less or little zoning, doesn't provide an animal shelter, and has a much more limited library facility. Hattiesburg proper has a wonderful library.
That being said there are many who will tell you you must settle in Oak Grove because the school system is better. Actually, the school system has more educated and professional families thus it performs better while the city schools have a very large population on free lunch programs. This economic difference, as so many studies suggest, affects the academic performance levels of students.
If my child were in school now, I would want him to go to a higher performing school with peers who have the highest aspirations and goals. It is sad but the shift of school-age families with means and education to the outskirts or private schools has significantly changed the demographics of the city schools. For me, I prefer the diversity of a city school but I think a higher percentage of poor performing students has to affect the overall academic quality within any individual classroom, the quality of teachers, and the ability of the school to offer enrichment.
If schools are not an issue you have many choices, rural, suburban, gated, and in-town neighborhoods.