All depends on how much time you can afford and what you like to do but no less than 5 days. 

In Ine lake, i suggest you to visit to the morning market, Phaung Daw Oo Pagoda, indein, villages with stilted houses and floating gardens built up from strips of water hyacinth and mud and anchored to the bottom with bamboo poles. You will also see the leg-rowing fisherman who steer their boats with incredible balance. 
In yangon, i’d recommend Shwedagon Pagoda, Kaba Aye Pagoda, Lady House, Bogyoke Aung San Market, Sule Pagoda, Sakura Tower
Have a nice trip!
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