Hi Icey. I have stayed at the Nana hotel plenty of times, though I also know nothing about LBs. I do know a thing or two about being alone in Bangkok though.
The Nana is a bit 'low rent', which is fine for me. It is a little old and tired, but we all have our problems. They are switched on though, guards will check in your company so they will know who is in the hotel, this is a good thing because it means you are fairly safe. You need your hotel to be awake.
I think that being alone in Bangkok is like being alone in any big city, you are a target to an extent so you need to be aware.
Taxis are very cheap in Bangkok and the best way to get around the city.
Enjoy your trip
