Starbase 97
Starfleet facility commanded by Admiral Mitchell. Commander Calvin Hutchinson served for some time there, prior to his assignment to Arkaria Base.
  "Starship Mine" - TNG.
Starbase 103
Facility located a short distance from planet Minos. After ordering a saucer separation maneuver at Minos, Geordi La Forge instructed Engineer Logan to proceed to Starbase 103.
Of course, even if Starbase 103 was only a few light-years from Minos, it's unclear as to what purpose there might of been in heading toward the base, since the saucer section had no warp-drive capabilty.
  "The Arsenal of Freedom" - TNG.
Starbase 105
Starfleet facility. In the alternate history created when the Enterprise-C vanished from its proper time in 2344, Starbase 105 was a possible destination to which the Enterprise-C could of been escorted.
  "Yesterday's Enterprise" - TNG.
Starbase 117
Site to which the Enterprise-D sent two members of the Ferengi Trade Mission, following their part in an accident that befell Kriosian Ambassador Briam in 2368.
  "The Perfect Mate" - TNG.
Starbase 118
Facility where the Enterprise-D picked up several new crew members in 2369.
  "A Fistful of Datas" - TNG.
Starbase 123
Starfleet facility that detected two D'deridex-class Romulan warbirds on an intercept course with Tin Man just prior to contact with that life-form in 2366.
  "Tin Man" - TNG.
Starbase 129
In an alternate quantum reality visited by Worf in 2370, the Enterprise-D set course for Starbase 129 following significant damage to the secondary plasma conduits caused by an attacking Cardassian vessel. Attacked by the Dominion.
Seen on a LCARS causality list.
  "Parallels" - TNG.
Starbase 133
Site where the Enterprise-D docked in early 2367 for scheduled crew rotation. Dr. Dalen Quaice was posted at Starbase 133 prior to his retirement to his homeworld of Kenda II. The destination of the Enterprise-D after its mission at planet Delta Rana IV.
  "Remember Me" - TNG. "The Survivors" - TNG.
Starbase 137
During his sophomore year at the academy, Benjamin Sisko spent a field-duty assignment on Starbase 137.
  "The Ascent" - DS9.
Starbase 152
The Enterprise-D traveled to Starbase 152 for inspection and repairs following contact with Tin Man in 2366. The Enterprise-D had been seriously damaged in that encounter.
  "Tin Man" - TNG.
Starbase 153
Facility from which special Federation Emissary K'Ehleyr was launched, inside of a modified class-8 probe, for a critical rendezvous with the Enterprise-D in 2365. Attacked by the Dominion.
Seen on a LCARS causality list.
  "The Emissary" - TNG.
Starbase 157
Federation starbase that received a distress signal from the USS Lalo NCC-43837 after it suffered an attack from a Borg vessel in 2366.
  "The Best of Both Worlds, Part I" - TNG.
Starbase 173
Space station facility located in Sector 23, near the Romulan Neutral Zone. Site of legal proceedings establishing the sentience of the android Data. Captain Phillipa Louvois served on Starbase 173. Also at Starbase 173, engineering officer Ensign Sonya Gomex was among several new crew personnel transferred to the Enterprise-D.
Starbase 173 was a reuse of the Regula I space station model originally seen in Star Trek II.
  "The Measure of a Man" - TNG. "Q Who?" - TNG.
Starbase 179
Planetside facility. The Enterprise-D visited Starbase 179 on stardate 42506 in 2365 for personnel rotation and to pick up Ensign Mendon as part of an Officer Exchange Program.
  "A Matter of Honor" - TNG.
Starbase 185
Facility that was nearest to the Enterprise-D after Q transported the vessel across the galaxy to System J-25. Data estimated the starbase was some two years, seven months away from the ship at maximum warp.
  "Q Who?" - TNG.
Starbase 200
Destination of the Enterprise in 2267 when an unexplained time-warp distortion was encountered. This distortion caused complete disruption of normal magnetic and gravimetric fields in every quadrant of the galaxy.
During the original Star Trek series, Starfleet supposedly had only 17 starbases. This was one of the few starbases in the original show that broke that rule.
  "The Alternative Factor" - TOS.
Starbase 201
Site where an orphaned Jem'Hadar child was to be taken in 2371.
  "The Abandoned" - DS9.
Starbase 211
The USS Phoenix NCC-63420 was escorted by the Enterprise-D to Starbase 211 following Captain Benjamin Maxwell's unauthorized attack in Cardassian space in 2367.
  "The Wounded" - TNG.