Formal:
* Contiguous: Sharing a common boundary or edge.
* Adjoining: Lying next to or close to.
* Neighboring: Located near or next to.
* Abutting: Touching or bordering.
* Proximal: Situated near to.
Informal:
* Next to: Simple and direct.
* Beside: Similar to "next to", but implies being close at hand.
* Alongside: Alongside or parallel to.
* Near: A general term for proximity.
The best synonym for "adjacent" depends on the specific context of your writing.