Sri Lanka is unusual in that it gets TWO monsoon seasons, from May to September the south west coast is expected to get the rain and wind, while from November to May the east coast gets it.
Most tourists spend most time on the south/west coast, so one would expect that July-August might be not good.
HOWEVER...
I've been to Sri Lanka a number of times, and stayed on that SW coast at different times of year. In May, June, July, and August I've had some wonderful hot sunny days. There were some short rain bursts - but they were short and infrequent, and the sun came out immediately afterwards and everything was dry in minutes.
Also I went in November once when, according to the travel books it should have been dry - and that time the island was hit by a tropical cyclone - and that WAS a windy wet time!

Where to go? Most first-timers to Sri Lanka have some time in a beach resort, and combine this with a few days touring places like Sigiriya, Polonnaruwa, Pinnawela Elephant orphanage, and further inland to Kandy and Nuwara Eliya. It is an amazing destination - there's lots to see.

One really amazing spectacle which you should try to see if you are on the island at the right time in July/August, is the Kandy Perahera - a couple of days of incredible processions at night, with hundreds of elephants, dancers, and flaming torches. I've never seen anything like it anywhere else in the world.
One minor snag is that alcohol is not sold in public areas during the Perahera, though there are some enterprising locals who do manage to sell mysterious can shaped brown paper bags to tourists while carefully watching out for the police!

A couple of other Sri Lanka unique points - on full moon (poya) days, alcohol is not supposed to be sold anywhere. And if you are a wine drinker, you will find it is very expensive on the island, though all other alcohol is very cheap.

Have a great holiday!