Tbilisi is very safe after the Rose Revolution. The police system was reformed completely and the recent polls show that public's trust in police shifted from nearly 10% to 88%. The police are usually quick to respond, though usually only Georgian and Russian are spoken.
While walking is generally fine, even for solo women, it makes sense to take a bus or taxi home at night. Use common sense and big-city awareness. Night time at the clubs and bars are safe, and taxi service is safe as long as it's a company taxi like "009" or others. The public bus is also a good, safe option for 0.50 lari.
Police Tel: 022. or 112 from Mobiles.
Ambulance tel: 022 or 033 or 031.
cope
You should make a quick stop in the Tourism Office on the south side of Freedom Square upon arriving in Tbilisi. They provide a free, very detailed map of the city as well as varying levels of competency when it comes to information; they are often out of printed material, and it can take some time to extract maps, brochures, etc, as they keep most of these hidden behind the counter and are often oddly reluctant to part with them, though if you're politely persistent you may be able to get what you need. They can print out a list of hostels or hotels upon request. August 11, 2011. For now, the tourism office is located in the Georgia Museum of History at 3 Rustaveli Street. It seems like they are doing repairs on their normal office.
Stop by the Marriott Courtyard if you're lost - the staff are fairly fluent in English, and they are more than happy to provide you with free maps, and help you track down whatever you're looking for on a map before you leave.
When all you want is to order food in English and not be bothered, head to the Marriott Courtyard, though the food does tend to be quite expensive. Head to Prospero's bookstore on Rustaveli 34 for a delicious, if relatively pricey 5-7 lari chicken salad sandwich and great coffee of every variety. Good selection of books and a nice calm place to escape, just a little.
Be careful about renting DVDs from Prospero's bookstore - there is quite a selection, but as most of them are pirated, almost half of all their DVD stock is of a poor quality. For your peace of mind, you can check any DVD on a player in the cafe before you rent it.
contact
There are 3 GSM operators of mobile phone service:
Magticom: provides 3G
Geocell: provides 3G, covers all of Georgia, packet data deals available for prepaid
Beeline: russian company, the cheapest of all sim cards, but does not get the best reception in some areas. buy a sim card at the office on Rustaveli Avenue or Ortachala international bus station help-line number for Beeline mobile: 110101 from Georgia.