a little problem in Sunny Beach with the rain as there's not loads on offer except for bars/restaurants/hotel. There's certainly nothing of note worth visiting like museums, ruins, castles etc.
Many of the hotels offer internet connections with game installed.
Nessebar offers plenty of interest with partial cover. There are plenty of churches (over 40) most of which have been converted to art galleries some of which are very interesting others rather amateur. Nessebar is celebrating 50 years of art/church (not sure due to language barrier).
The mountains nearby might offer some respite from the rain whilst offering great views and some local life. However you should be aware of ticks: http://www.holidaytruths.co.uk/viewtopic.php?t=82258
Bourgas or Varna offers the usual city entertainments. I wasnt in Bourgas for long but found it inviting and cheap. There's a few attractions but we settled for a cafe watching the world go by.
Strange as it may sound the beach still offers plenty for the adventurous during the rain. Nessebar would be my choice with some snorkelling. There are huge mussels and sea snails (conks) in abundance here, plenty of fish and much evidence of octopus. When the rain falls you'll actually find its quite warm as long as the sea breeze doesnt blow too hard. As my Dad used to say "get under the water and you won't get wet".

Hope you manage to entertain them.

hi there is a bowling alley in the globus hotel i forget how many lanes i think 4or 5,its also got some electronic games.there was also a large bowling alley along the main road,don't know if its still there though.

when are you planing on going, the weather forcast for the next 10 days is supposed to be sunny?

Going 27th to 4th sep. The weather forecasts i have found (using peter of yorks links on a different thread show a good chance of thunder and showers on mon and tues then sunny for the remainder. If you could provide a link or address of the good weather i would be vey grateful!

Thanks for the other replys re things to do , as long as it's only wet for a couple of days i don't really mind. I think the suggestion of using the beach anyway is fab,I've never swum in the rain before sounds fun, should be a lot less crowded too! ( Although prehaps not if there are thunderstorms.)

Many thanks, Tunise.

Try THIS link. No rain forecast up to 6th September.

Peter

Peter of york- many thanks, i shall keep my fingers crossed! Isn't it amazing that forecasts vary so much. Tunise

AccuWeather.com - Varna 15-Day Forecast,try this one

Thanks Suemackey.

hope its more reliable than the one that forecast a heatwave in england for august

They might use seaweed of a higher quality!

Peter

The Sea Gardens in both Varna and Bourgas are nice (although it depends on how heavily its raining!)

I really liked the history museum in Varna too (about 2 hours from Sunny Beach on the local bus). It takes a while to go round - but your enjoyment would probably depend on how much your kids are into gladiator battles and ancient Greeks/Romans. There's also the remains of a Roman baths and a couple of other musems - they're in the Lonely Planet guidebook (I've left mine out).

There's also a dolphinarium in Varna (and it runs in my mind that there's a reptile house nearby, although I can't quite remember for sure).

There's a museum in Bourgas but its not as good - although its good to duck into if you get caught in a thunderstorm. The curator only speaks English and German though, but if you've got a few words in either of those then you should be ok.

we were there same time last year, it tends to only rain at night/ evening. I think you'll be ok.