"I saw Sue in town yesterday, but she didn't see me." Why is there no article before "town"?

In town here uses a special sense of town, which refers to whatever is understood to be the local region. Saying someone is in town is akin to saying they are in the neighborhood or in the area; as the LDOCE has it:

where you live [uncountable]: the town or city where you live:

Cam left town about an hour ago, so he should be out at the farm by now.
I'll be out of town for about a week.
Guess who's in town? Jodie's sister!
Do you know of a good place to eat? I'm from out of town (=from a different town).
We're moving to another part of town.

• To say Cam left town means he departed from the local area, or from wherever area he had been before. To say Cam left his town means he departed from (perhaps abandoned) his hometown. To say Cam left the town means he departed from some particular settlement which is known.
• If you live in town, it means you live in the local urbanized area, as opposed to living in the suburbs or in the country for the outlying areas.
• You can be out of the town but not out of town— that is, you can be physically outside the boundary line of a jurisdiction that is called a town, but you have not left the larger area.

There are other locations— mostly institutions— where dropping the determiner changes the meaning, like being in hospital or out of school; writing from prison or at sea; or going to church or to court.

See for example Which nouns should include an article after "go to [noun]" in AmE and BE? and Is there a reason the British omit the article when they "go to hospital"?.