Hi there joo
First of all check out the website for the bus company that runs between Halkidiki and Thessaloniki : http://www.ktel-chalkidikis.gr/index.php?act=viewCat&catId=1029 This links shows the timetable specifically between Kalikrateia and Thessaloniki.
As you can see there are many buses running daily.
April is indeed not a great month for many activities, however the beach in Kalikrateia is a long one, so you can have wonderful long evening walks, there is a weekly open air market which it'd be nice to visit and get the local feeling. Lots of cafes and restaurants will be open anyway, as Kallikrateia has around 10-12.000 permanent population. Petralona is a fantastic cave which is a must see I think, especially for kids. It's not that far away from there, but it'd be better if you make a call from your hotel first to the cave , inorder to make sure that it will be open and schedule it.
Since there will be four adults, there is also a great winery that you could visit, at the area of Epanomi, again not very far from there. It's called Ktima Gerovasileiou.
Then as far as Thessaloniki is concerned, it's the city that you can find literally EVERYTHING! Great museums, beautiful arcaeological, and not only, sites to visit. FANTASTIC food and cofffee places, great shopping experience. It's generally a very lively city that can cover all tastes I think . The city's new waterfront, from the White Tower (city's trademark) all the way to the Music Concert hall on the east side of the city, is a fantastic place to walk, rent a bike, have a coffee, enjoy the views, relax under the shades of big trees etc.
Hope that helps for now.
Enjnoy your holidays at the area.
Giannis.