How long your cycle lasts depends on the amount of LR
and sand...and that length of time will be determined by your ammonia/nitirite/nitrate levels which you will be needing to test for.
What kind of reef are you planning on having...if you are planning anything besides housing softies in this tank you are going to need additional filtration to keep your water pristine. Doing this in a small tank like a nano can be difficult. I would highly suggest a sump/fuge setup to aid in nitrate removal and also a protein skimmer. This will prevent your nano from becoming toxic for your corals. Will save you a ton of money in the long run.
I made a mistake in my 55 gallon reef and it killed 500 dollars worth of coral. I still haven't got it squared away after a week, it is very frustrating. Hope this helps, if you have additional questions I'll do my best to help out, as will others.