My friend, I've stayed at the Marriott no less than 20 times and taken the shuttle double that, and it has never taken more than 10 minutes with 5 minutes being pretty much routine. The Marriott is located just a 100m from Syngrou-Fix metro station which is just 1 station away from Syntagma. We are talking less than 2 kms in total distance from the hotel to Syntagma. It never takes 40 minutes. Perhaps from the Hilton to Syntagma, that would be accurate, but not from the IC and Marriott. It's extremely close to the centre. If you are up for a stroll, then you can walk from the hotel to the Acropolis which would take perhaps 15 minutes straight up Syngrou Avenue. If you are up for taking the metro, as I said, Syngrou-Fix metro station is just 100m up Syngrou Avenue. This line runs to Piraeus and to Syntagma and northbound. It's very cheap at 80 eurocents for a ride.
The Grande Bretagne is an amazing hotel. I did use points to spend 1 night there and it was absolutely wonderful. However, I would never pay the prices they charge to stay there. It is a great hotel, but way overpriced in my opinion.
The OP made specific mention of beach, so I assume in warmer weather. I mean, afterall, the islands are pretty much shut down from October to March anyway. Current high seasons with all the major hotels is running from 1 July to 30 August. Sheraton is offering specials for May and June if you are keen on paying for it. However, I still stand by my suggestion that if you prefer to go on the cheap and use points, a Coupon Connection trade with someone who has alot of SPG points is an ideal way to go. Of couse, this is only my personal opinion.
There is an interesting website for expats living in Greece. It often has interesting places to go and see. I would recommend taking a browse through some of the archived issues regarding beaches if that is your main goal. http://www.xpatathens.com/
Efharisto.