Yeah I think they need to encourage people to come and join the party, rather than warn them away.
Sydney is the perfect example of how to host the games - venues spread all over Sydney's greater metropolitan - right to the blue mountains, as far south as campbelltown and everywhere in between. Every 'event host' city council had their own little expos to encourage tourism and visitation. I personally worked on the expo put on by Penrith City, with the rowing and whitewater venues, and the equestrian events just down the highway. Homebush was a non-stop party, and Sydney did an excellent job of managing the transport requirements.
Sydney also didn't suffer the 'white elephant' venue problem that many other countries have experienced - a new stadium that became regularly used as a home ground for several sport clubs, coupled with the ancillary venues surrounding it that is regularly used for events, concerts, the royal easter show etc. Many of the other venues continue to see regular use today including the baseball fields, equestrian centre and regatta centre. Even the athletes village was quickly converted into much needed housing for the area. (and the OLYMPIC LOGISTICS CENTRE SALES WERE CRAAAAAZAAAAAY! (Anyone remember those ads?))
The biggest thing that Brisbane (and the greater surrounds including the Sunshine and Gold Coasts) needs is transport infrastructure to manage the load. Our current train network is abysmal. The busways are ok, but the Pac motorway and the Bruce Highway aren't up to coping with any massive amounts of additional traffic the moment someone drops a spanner in the works.
Everything for Brisbane is geared around the Brisbane CBD - if i'm in Coopers Plains and I want to travel to Darra - a train needs to go all the way to Roma St for me to interchange with the Ipswich or Springfield line. Everything is a line straight to the city. All of the interchange stations are one of the central areas close to the river, ergo the CBD.
Honestly - relocating the Ekka into a greenfields space - perhaps up near boondall near the entertainment centre - doing a 'homebush' and creating a space that is - connected to arterial highways, out of the city gridlock, able to be easily connected to public transport hubs, and you're on a winner. Build a stadium and an arena, as well as supporting facilities to host a multitude of events (oh, and it won't flood like Suncorp)
At least in Sydney, you can pretty much get anywhere on the network without going through the city if you need to.
On topic - as Brad mentioned i'm fairly certain the parks will continue to add their usual attractions, although timing the opening of something close to the games wouldn't be a horrible idea.
Wonderland did see an uptick in visitation during the games - but they were using the Wonderland carpark as park-and-ride parking for other event venues too. I think overall, tourism does see an increase - athletes, and their supporters are usually in town for the duration of the 2-3 weeks of the games (and more in preparation) but their events don't usually last the entire games, so they have a lot of time to explore - especially the fans who don't have to worry about training.
TL:DR - Sydney was an absolute party, non stop, for the entire duration of the games. Everyone got on board, and there was no messaging to stay away, because the infrastructure could handle the load. They did everything right (although they started with a pretty good public transport network to begin with) and everything was designed for more than a single event use.