The beaches to the southwest or those in the vicinity of Galle are best visited in mid-December through the end of February. This includes Hikkaduwa, Unawatuna, Mirissa and even Tangalle. This area is also good from mid-July through to mid-September in terms of relatively low rainfall, but the sea can be quite rough then, so it does limit your ability to partake in water activities. Outside those times, the beaches are still nice, but occasional winds can still make the seas rough and choppy.
The east coast — including the popular surf spot — Arugam Bay is quite nice from June to mid-July and then very good until late September. From October through to mid-December this area is still quite nice, but there can be sustained rain. From mid-December to February, it is not advisable to visit this area for beaches.
The northeast coast including Trincomalee and Batticaloa has experienced some development and there are some nice places to stay. It is, however, sparsely populated and could use some trees.
Mirissa is a popular surfing spot and is also a calmer area than Tangalle which has quite rough surf. There are various operators offering surfing lessons and there are lots of boards for rent. Mirissa has a collection of properties to choose from that are mostly along the beachfront or just slightly back from it. There are a couple of properties that are trying to position themselves at the high end of the price/service/comfort spectrum, but the bulk of accommodation here is cheap and cheerful and is very good value for much of the year. Mirissa is a great place to learn how to surf if that takes your fancy.
The geography here makes for some lovely coastal scenes. Rocky cliffs and outcrops with crashing surf. The resorts in this area are either large scale and a tad institutional, or are a budget level wooden bungalow. Having said that, there are new places opening all the time, so the possibilities continue to grow.
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Probably the best option if you want premium resorts/accommodation, picturesque beaches, and accessibility to Galle. It's only a 15-minute drive over to Galle Fort. In addition to the larger resort properties, there is a good range of Villa properties that are great for medium to long stays. There are also a couple of fantastic beachfront restaurants in this area.
One of the longest established tourist beach areas in Sri Lanka, Hikkaduwa offers a lot of activity, good nightlife and some laid back, tastefully designed accommodation. The beach is a little tatty these days with lots of restaurants, bars, and guesthouses along the shore and then the busy Colombo-Galle Road ripping through the middle. It is, however, a good place to surf in March, a good place to Kitesurf and there is a reef just offshore, so you can go snorkeling and your chances of seeing turtles are fair to medium.
Arugam Bay in the southeast of the island has a really interesting vibe. It is undoubtedly a surfing hangout and hence experiences pronounced seasonality in visitor volumes. Accommodation in Arugam is almost entirely at the budget end of the spectrum. There are better beaches if you don't surf, but if the seasons match and you are in the neighborhood, maybe wanting to visit Gal Oya National Park also, then it's a fine place to visit. There is some nice riding/walking/trail running in the hinterland just nearby, although there is a bit of an Elephant hazard at times apparently.
Batticaloa & Trincomalee
Trinco is probably the most appealing of the two locations considered the Northeast. These are mostly Tamil areas which makes them culturally quite different from the southern beaches, which are pretty much all Sinhalese areas. The beach is nice, and most importantly is largely bereft of beach bars, crowds and people trying to sell you things. There are some decent resorts that have opened in recent times and Trinco is only two hours or so from the Cultural Triangle area. The motivators for visiting these locations are likely to include the weather and proximity to the Cultural Triangle if you are aiming for a compact trip.