If you dont mind man made beached then head into the City. Southbank has a great swimming facility that is only 25 minutes or less away from Algester. Need to get into the surf, then the best types of beaches are found down at the Gold Coast. Well worth the drive and a great day out.
The closest Beach to Algester for swimming would be to travel 40-45 minutes down the highway to the Gold Coast. Or if you want less of the swell you can go out to Wynnum/Manly coastline which is nice also, especially down at the marina.