Baku 
Gyanja 
Naxcivan 
Mini-buses (marshrutkas) are great to get around the country. They're cheap and the leave frequently. The night train between Sheki and Baku is a popular alternative way to do the trip.
From Baku, you'll find direct minibuses to Seki. There are no direct buses from Sheki to Tbilisi. It often involves several changes. Try to get to Zaqatala and change there for the border. Then another change at the border. There is no "visa" for Georgia. Just a stamp.There are no direct buses from Sheki to Tbilisi.
There are however direct buses Sheki-Balakan (Azeri side of the border) which are limited to a few per day. Optionally, you can hop Sheki-Qax-Zaqatala-Balakan by frequent marshrutkas. Though time consuming there is nothing difficult and no thorough planning is required. Buses heading towards Balakan and beyond will make a stop in Zaqatala.
From Balakan to the border, take a shared taxi (the cost is around 1-2 euros per seat). Once in Georgia, you're about 4 kilometers from the center of Lagodekhi. You'll either have to take a taxi (but ask around and do bargain) or walk. From Lagodekhi's center, you'll find minibuses to both Telavi and Tbilisi. It's 150 km to Tbilisi and the journey will take about 1.5 hours by car or 2-2,5 hours by bus.
From Lagodekhi (Georgian side of the border) to Tbilisi buses are frequent, they run every 30 mins or so.
The same way you can go from Tbilisi to Baku!
Mashrutka Seki - Zaqala.......less than 2 hours
Mashrutka Zaqatala - Balakan.........about 1/2 hour.
Lagodekhi-Balakn border crossing is a pretty quiet frontier, with little traffic. It closes at night. Because it's quiet, foreigners present some amusement for the guards and you might find yourself the centre of attention for a friendly but inquisitive cluster of them.
On the AZ side, you are met at the first gate by an armed guard who checks your passport before admitting you to the enclosure and passing you to the customs officials. Someone will ask you whether you have anything to declare and then a group will gather around a bench to watch a cursory examination of your bags. You are then sent to the immigration window, where the official will riffle thought your passport several times (looking for evidence of travel to Nagorno-Karabakh) before stamping it. When you walk to the guard at the last gate, he will radio back to the office that's 15 metres behind you to confirm that you're cleared to pass.
Across the bridge, the first Georgian guard will check your passport before directing you to the immigration and customs office. You will pass an exchange office just before you get to it -- the rates are quite good. Inside the office, an official will riffle through your passport several times (perhaps looking for evidence of travel to Abkhazia) before stamping it. Your bags are X-rayed and then you walk out past the final guard who will look at your passport once more. The Georgian guards are more aloof than the Azeri guards but also convey discipline and rectitude.
Planning your trip: Qusar makes an interesting day-trip from Quba. It'll help you better understand the incredible linguistic diversity of the region (the people of Xinilaq, Quba, Krasny Slovoda, and Qusar each speak a different language, though all 4 towns are startlingly close) and it's interesting enough for a day. People are friendly and will probably try and teach you some Lezgin. Sheki is lovely, and Kish is certainly worth visiting as well. On the way from Sheki to the Georgian border, there are two towns of note: Zaqatala and Balakan. Zaqatala is very pretty; it's a good town to stay the night in. Balakan has little to offer besides a beautiful old minaret - it's only a couple of hundred meters off the main road, and worth visiting on your way to Georgia, though might be not a great overnight stop.
