First the capital. Tablisi. Tablisi is home to many hot springs and draws its name from the old Georgian, 'tpili' which means 'warm'. The story goes that in the 5th century, Georgia's King Vakhtang GorgasaliIt chanced upon the hot water springs which were at that time covered under a dense forest. He was so impressed by the hot springs that he had the forest cleared and a town built around the hot springs. He named the town 'Tpili' or 'Tbilisi'. The name is interesting. Firstly, Georgian 'tpili' is obviously derived from the Sanskrit 'tapa'. There are many rivers in India such as the 'Tapati' and the 'Tapi' that get their name from the root word 'tapa' (तप) which means 'warm'.
In the Georgian annals King Vakhtang's name is said to be derived from Iranian 'vahrka-tanu' meaning 'wolf-bodied', a possible reflection of the wolf cult in ancient Georgia. But it is interesting that the Iranian 'vahrka-tanu' is the same as the Sanskrit 'vrika-tanu' (वृक - तनु) which has the exact same meaning - wolf-bodied. But at this point, Sanskrit can bring in a correction for a more accurate interpretation of the name Vakhtang. The name of the King should either have been Vrka-ang (wolf-bodied) or Vrka-anana (Wolf headed). Legend says that King Vakhtang wore a wolf's head as a helmet during battle.
The city of Tablisi lies on the River Kura. It is said the river gets its the name from Cyrus the Great, the emperor of Persia, whose Persian name was 'Kurus'. (Cyrus was the Greek interpretation of 'Kurus'). His name is akin to the name of the 'Kuru' (कुरु) dynasty of the Mahabharata. This connection is not too far fetched considering that in the ancient Iranian annals Kurus's father's name is recorded as the Sanskritic 'Kambhoja' (काम्बोज), though the Greeks later recorded his name as Cambeses.
In India, the name 'Kambhoja' is first attested in the later Brahmana stage (7th century BC) in the 'Vamsa Brahmana', as well as in Yaska's 'Nirukta'. 'Yasaka' was an ancient Sanskrit Grammarian who wrote the 'Nirukta' - a book that details the etymological sources of Vedic words and sutras (rules) that operate when deriving the meanings of Sanskrit rules. 'Yasaka' (5th-6th century BC) preceded the better known Sanskrit grammarian Panini (4th century BC).
Some have contented that the River Kura gets its name from the ancient Albanian term for 'reservoir'. Once gain the Sanskrit connect is evident. In Sanskrit, 'karshu' (कर्षू) means 'river', so does 'kula' (कूल) which is more often used to refer to a 'river bank'. A 'kupa' (कूप) is a 'well' and 'kulya' (कुल्या) is a small river. Derivatives of 'kula' such as 'kulini' (कूलिनी) and 'kulvati' (कूलवती) also mean 'river'.
It is also be possible that River Kura gets its name from that of the Kolchi inhabitants of ancient Georgia. The Kolchis were a dark skinned race and there name is possibly derived from the Sanskrit 'kala' (काल) meaning 'dark' or 'black'.
The Georgian endonym of River Kura is Mt'k'vari and is traced to the Georgian 'good water'. That too has a Sanskrit connect, for 'vaari' (वारि) and 'vaarii' (वारी) mean 'water' in Sanskrit. The first syllable could be a distortion of any number of words from Sanskrit.
At the centre of the city of Tablisi is Mt. Mtatsminda. Mtatsminda Mountain is translated as 'Holy Mountain' from Georgian. Sanskrit throws additional light on its name. 'Mtat-sminda' is a cognate of 'math-sumedha'
(मठ्-सुमेध) which means 'Temple of Purity' in Sanskrit. This may be seen in the context that the ancient name of Mt. Everest is 'sagar math'(सागर-मठ्).
Mtastsminda is also the seat of what is today know as Narikala fort. The fortress was established in the 4th century and its name was 'Shuris-tsikhe' and translates from Georgian as 'Formidable Fort'. In Sanskrit 'Shura' (शूर) means 'brave, warlike, daring' and hence is the equivalent of formidable. 'Tsikhe' is a cognate of the Sanskrit or 'shalaka' (शलका) which means 'rod'. But whether the 'rod' and 'fort' are connected is not clear at this point.
Another fort by the name of 'Upalistsikhe' translates from Georgian as 'Lord's fortress. In Sanskrit 'upalaksh' (उपलक्ष्) means 'distinguish'. Upa' (उप) by itself means 'above' or 'top'.