Thank you for using History Hub. There indeed is information about US post office locations in the 1830s but there are various ways to find it depending on what kind you want.
At the National Archives building in downtown Washington, DC we have three microfilm records series in Record Group 28, Records of the Post Office Department, that will give you some information. Two of the series cover dates before 1833 or after 1836 but could still prove useful. These would represent an on-site, brute force research effort.
Perhaps the most relevant series is M841, Record of Appointment of Postmasters, 1832-Sept. 30, 1971. These records are arranged alphabetically by state, thereunder by county, and then by name of post office. In addition to location information they provide dates of establishment and discontinuance of post offices, the names of postmasters, and dates of postmasters' appointments. This series is available on the commercial website Ancestry.com. If you do not have a subscription, many libraries and historical societies do. You can find it simply by typing “M841” into the search bar.
The page for series M841 explains that there may be active post offices described elsewhere in series M1131, Record of Appointment of Postmasters, Oct. 1789-1832 . Furthermore, the information gleaned from this research could be cross-referenced against series M1126, Post Office Department Records of Site Locations, 1837-1950, which are records of post office locations. Contact the Archives I reference branch at email@example.com for more help. We also suggest contacting the NARA cartographic branch in College Park, MD, which may have maps or architectural drawings if that is your interest. They are reachable at firstname.lastname@example.org.
Apart from this method a search on Worldcat showed several publications from the mid to late 19th century with contemporaneous lists of US post offices. It seems as early as 1846 that the government published lists of post offices. Even if you’re looking for more than simple lists we suggest contacting a Federal Depository Library in your area.
Best of luck to you in your research. If you find what you’re looking for, we’d love a follow-up on this thread!