Where on Earth does paleo-groundwater exist?
In large intracontinental basins where the main rock formations are exposed in adjoining highlands and rare deeply buried within the basin itself.  The Madison Limestone is an example.

The Madison and its equivalent strata extend from the Black Hills of western South Dakota to western Montana and eastern Idaho, and from the Canada–United States border to western Colorado and the Grand Canyon of Arizona.

From Wikipedia.

Ground-water ages vary from virtually modern to
about 23,000 yr. The 14C ages indicate flow velocities of
between 7 to 87 ft/yr. Hydraulic conductivities based on
average carbon-14 flow velocities are similar to those
based on digital simulation of the flow system (Downey,
1984).

From: Geochemical Evolution of Water in the
Madison Aquifer in Parts of Montana,
South Dakota, and Wyoming
By JOHN F. BUSBY, L. NIEL PLUMMER, ROGER W. LEE, andEWJCE B. HANSHAW