Sorry if any of the below comes across as negative in advance! We went to Sri Lanka this Easter and travelled around - I loved it. It’s a beautiful country and the people are quite exceptionally kind. The weather was just starting to change when we went and as I’m sure you know, summer is monsoon season. The general recommendation is to go East of the country in the summer to avoid the bad weather. We did have a bit of rain when we went and it absolutely pelts down hard.
All the families and tourists we met were either on tour company coach tours or had hired drivers. I know some people do travel around by public transport though, particularly using the trains. The roads (with the exception of one or two motorways) aren’t great and going anywhere does take some time. For example, it took us 4-5 hours in traffic to get to Kandy from Colombo. Dambulla and Sigiriya were another couple of hours on from Kandy, i don’t think either would be do-able from just north of Colombo which would be a shame to miss. Kandy would be a do-able day trip from Colombo (although it would be a long day!), There is a big religious festival in August at the Temple of the Tooth which would be worth seeing. It does involve an elephant being ridden though so depends on what you feel about that and I imagine the traffic to and from the city will be choc a bloc - there is a Kandy/Colombo train though.Avoid the Pinnawala Elephant Orphanage which is a frequent stop off on the way to Kandy, from an animal welfare perspective it’s not ethical.
We had a day in Colombo - it’s sprawling, not the loveliest and the traffic is absolutely horrendously mad. There are some historical sights but it’s not somewhere i think I’d go back to if I went to Sri Lanka again.
We didn’t go to Galle but that’s another possible day trip and a motorway connects Colombo to Galle. It’s an old Colonial city on the coast.
I’d go on Viator, put in ‘day trips from Colombo’. That will give you some ideas of what is going to be do-able. If you’d like their details, happy to pass on the contact details of our transport firm who I’m sure would quote you better prices for the same trips.
I’m not an AI fan so this might have coloured my response - I just think because of the slowness of travel in SL you’re going to miss out on seeing some great places and trying a good variety of food. I don’t think the weather at that time of year is going to be ideal for days flopping around the pool either (although I’m sure you’ll get some sunshine). Apologies OP, this is all just personal opinion. As above, it’s a brilliant country and I’m sure you’ll have a great time.