Depending on which hotel you're staying at you can probably take the hotel's shuttle from the airport. The taxis will take you there too.

Once you've checked in and need to go anywhere have the concierge write the address for you to show the cab driver in case his English is not so good which it will probably be.

Shopping is divided into two categories; there are department stores with fixed prices and there are open-air markets and family-run stores at which you can haggle. It's expected so don't be shy.
By all means go to these markets, take in the sites and smells and enjoy your time.

Use common sense in terms of security. Always make a note of the cab number you're riding in, don't accept the cabbie's offer to take you somewhere special for shopping, fun, sightseeing and don't wander around an area where you're the only person there!

I always travel alone and have never run into a problem anywhere. Just be aware of your surroundings, keep your money safe, never have your wallet in your pocket (!) and don't keep your hotel's key card in the little pouch/wallet tehy give you with your room number in it. That way if you lose it or it's picked from your pocket people won't know what room to go to!

Enjoy it.