I anchor inside the lagoon all the time, so I disagree with @Jeffthornton's opinion about nobody here having experience.

The lagoon has two sides - the Dutch and French; both have different rules.

You can enter the Dutch side and drop anchor anywhere outside of the marked channels and the marked runway exclusion zone. There is not a huge amount of space available. My boat draws 8.5 feet so my options are very limited, but with a shallower draft you can almost always find a spot, even in high season. You can yellow-flag in and anchor before clearing in. The fees for the bridge and for staying in Simpson Bay are published and depend upon the boat length as well as the duration of stay. All of the mooring balls inside the lagoon are private and may not be used without permission. Some are available for rent. The bottom is muddy and there are shallow areas to avoid (I've help pull many a boat off the one close to the Dutch bridge).

The French side is much larger and there's a lot of room to anchor (although there are also a lot of boats). There is no weekly/monthly charge, so it is more popular with the cruisers and liveaboards than the Dutch side. There are mooring balls, but they are also private and cannot be used without prior permission. You can enter the Dutch side and then transit through the Causeway bridge; or use the French side bridge and channel if your boat draft (and nerves - the channel is narrow, poorly marked and shallow) is up to it.