Map from Google - Georgia

The climate of Georgia, mild and rainy on the coast and in the western plain, becomes more continental and arid in the central and eastern inland areas, while in the mountains it's obviously colder.
Here is a map with the three main climate zones.

Climates in Georgia

Along the Black Sea coast and in the western plain (zone 1 on the map), rainfall is abundant, amounting to 1,500 millimetres per year or more, and is distributed fairly evenly throughout the year, albeit with a maximum in autumn and winter.
Here is the average precipitation in Sukhumi, in the northern part of the coast.
Average precipitation - Sokhumi
SokhumiJanFebMarAprMayJunJulAugSepOctNovDecYear
SokhumiJFMAMJJASONDY
Prec. (mm)1151201101201001001101151351101301351400
Days131313131310109991011133

In Batumi, in the southern part of the coast, even 2,500 mm of rain per year fall, with a peak in autumn. Here is the average precipitation.
Average precipitation - Batumi
BatumiJanFebMarAprMayJunJulAugSepOctNovDecYear
BatumiJFMAMJJASONDY
Prec. (mm)240205135140801651802353152603002602515
Days131414141313141413111314160

Winter is fairly mild along the coast, since the average January temperature is about 5/6 °C; the sea mitigates the climate while the Caucasus in the north partially protects this area from the cold winds, but we must remember that beyond the Caucasus, there are the frosty Russian plains, so sometimes a bit of cold air manages to get here as well: on average there are about ten days with snow per year. Summer is warm or even a little hot, with an average around 22/23 °C in July and August; there's no shortage of sunshine, but as we said there are rains as well, and in summer they occur mainly in the form of downpour or thunderstorm.
Here are the average temperatures of Batumi.
Average temperatures - Batumi
BatumiJanFebMarAprMayJunJulAugSepOctNovDec
BatumiJFMAMJJASOND
Min (°C)345913171919161396
Max (°C)91011151822252522191511

This type of climate is also found in the plain at a short distance from the coast, in cities like Kutaisi and Senaki, even though here the summer gets a little warmer for the distance from the sea. In ancient times, this portion of the coastal and western plain was called Colchis.

In the interior (zone 2 on the map), separated from the western plains by some secondary mountain ranges such as the Likhi Mountains, we find valleys and plateaus lying at an altitude between 400 and 1,000 metres.
In the capital, Tbilisi, located in the valley of the Kura at 450 metres above sea level, the climate is slightly continental, and is much more arid than the coast. The average temperature in January is 2 °C, that of July is 25 °C. Here is the average temperature.
Average temperatures - Tbilisi
TbilisiJanFebMarAprMayJunJulAugSepOctNovDec
TbilisiJFMAMJJASOND
Min (°C)-2-1271216191915940
Max (°C)681218232831312620138

The rainfall amounts to 500 mm per year, with a minimum in winter, when 20/30 mm per month fall, even though the sky is often cloudy, and a maximum in late spring, of 75/80 mm in May and June, due to thunderstorms which can occur in the afternoon, and may occur, although rarely, even in summer. During winter, snowfall is quite frequent (although not abundant, because of the low level of precipitation), and also cold spells, during which the temperature can drop to about -15 °C. Summer is sunny, despite a few afternoon downpours or thunderstorms; there can be also hot days, with maximum temperatures around 36/38 °C.
Here is the average precipitation.
Average precipitation - Tbilisi
TbilisiJanFebMarAprMayJunJulAugSepOctNovDecYear
TbilisiJFMAMJJASONDY
Prec. (mm)202530508075455035403020495
Days456810966564471

Tbilisi is a windy city, and can experience strong winds quite frequently.

Tbilisi

The Caucasus Mountains (Greater Caucasus in the north and Lesser Caucasus in the south) and the secondary chains (zone 3 on the map) have an Alpine climate, more or less cold, depending on altitude, with heavy snowfalls in winter; there are vast glaciers above 3,500 metres, especially in the mountains of the Greater Caucasus, which are higher. The highest peak in Georgia is Mount Shkhara, 5,193 metres high. Precipitation is particularly abundant in the westernmost mountains: the Mtirala National Park, in the Autonomous Republic of Ajara, receives more than 4,500 mm of rain per year.
From the mountains, in the valleys and along the coast, a dry and warm down-slope wind, can blow from the mountains.

The sea is warm enough for swimming from July to September, and reaches 25 °C in July and August, which are the best months for a stay at the beach.
Sea temperature - Batumi
BatumiJanFebMarAprMayJunJulAugSepOctNovDec
BatumiJFMAMJJASOND
Sea (°C)1099111622252524201612

When to go

The best times to visit Georgia are spring and autumn, especially from mid-May to mid-June and from mid-September to mid-October. Since in the coastal area the autumn is very rainy, here you may prefer the spring. For swimming and sunbathing, and also for high mountains, the best period is of course the summer, from June to August, when it can get hot in Tbilisi and in the inland valleys, even though those who don't suffer from the heat, may choose this season to visit the whole country.

What to pack

In winter: in Tbilisi, the plains and the coast, warm clothes, sweater, jacket, hat, raincoat or umbrella. For the high mountains, mountain clothing, hiking boots.

In summer: in Tbilisi, light clothes for the day, sun hat, a light sweatshirt for the evening, possibly an umbrella for the afternoon rains; for the coast, light clothing, a light sweatshirt for the evening, a scarf for the breeze; for the mountains, spring/autumn clothes, sun hat, sweater and jacket, hiking shoes, raincoat or umbrella; mountain clothing for the highest peaks.