Over 90 nationalities need no visa for stays up to one year. Those who need visas can apply online and receive them by email.
Azerbaijan At the time of writing, the Tbilisi embassy is one of the most straightforward places to get an Azerbaijan visa, issuing 30-day visas within seven working days (often less). Take two photos, a passport photocopy and a hotel reservation (which can be an email from the hotel or a booking.com reservation). Fees are US$35 to US$60 for most EU nationalities, US$118 for UK citizens and US$160 for US citizens. Agencies near the embassy including Medea Travel will handle everything for you for about an additional US$50. The Batumi consulate is also well worth trying: its requirements and processing times fluctuate but travellers have obtained visas there without hotel reservations.
Iran The Iran visa situation was in flux at the time of writing. Thirty-day visas on arrival at all points of entry seemed likely to be made available to most nationalities. But UK, US and Canadian citizens still had not only to obtain a visa in advance but also to book a guided tour for their whole visit. This may well change. If you do need a visa, Tbilisi is a convenient place to collect it. You should apply several weeks ahead, through websites such as www.persianvoyages.com or http://caravanistan.com, for an Iranian foreign ministry authorisation code, costing around US$40. You nominate the Iranian embassy/consulate where you will collect the visa. Once you have the code, you go to the consulate, which in Tbilisi's case then sends you off to pay the visa fee at a bank (€30 to €200-plus for a 30-day tourist visa depending on your nationality) and return with proof of payment, your passport, two photos (women in headscarves), proof of insurance and your itinerary in Iran. Your visa should be ready the following working day.
Kazakhstan At the time of writing nationals of 36 countries need no visa for visits of varying periods (15 days for 10 EU states, the USA and Australia) – details at http://mfa.kz/index.php/en/kl-nlknlkna-lksn. Citizens of other EU countries, Canada, New Zealand and Israel can obtain 30-day tourist visas without a Letter of Invitation (LOI). The Tbilisi embassy normally issues these in three to five working days: get there at opening time as you'll have to spend about 45 minutes paying the fee at a bank.
Russia Travellers have obtained transit visas (normally for not more than three days for air travel or 10 days for land travel) at the Russian Interests Section of the Swiss embassy in Tbilisi, for US$60 with 10-day processing. You will need to talk to a consular official before applying, but required documents are likely to include proof of insurance and an onward visa. There is usually a knot of people crowding round the entrance to the building: push through and tell the guards you're a foreigner and need to ask for visa information. Thirty-day tourist visas may also be possible with an LOI, available via websites such as waytorussia.net.
Turkey Many nationalities don't need a visa for up to 30 or 90 days (see www.mfa.gov.tr/visa-information-for-foreigners.en.mfa). For others, e-visas are available rapidly online at www.evisa.gov.tr for between US$20 and US$80. Some nationalities can also obtain visas on arrival at Turkish airports or land borders; others can't. See www.evisa.gov.tr/en/info.