Hi,
I live in Vancouver and worked up at grouse for a couple of years so am pretty familiar with the place. You should go there for sure. Every stereotype of Canada in one place! Grizzly bears, birds in motion, lumberjacks etc. Not sure how great breakfast is but the experience is probably neat. Although you don't need the breakfast to see the bears. You should absolutely take the peak chair to the top of the mountain- the views are breathtaking! You could also do a biplane tour too which is pretty neat. In my opinion the eye of the wind tour is a waste. In fact it's actually pretty shocking. They installed the wind turbine before having an agreement in place to put it into the grid, and it's been a disaster. They claim 20-30% of all power on Grouse is offset. Good luck! It never spins, and in fact I've heard when it does they use electricity to make it spin. Anyhow, just my 2 cents!
If you didn't want to cab it there you can walk to waterfront and take the seabus, followed by the 236 bus directly to Grouse for way cheaper than a cab. But be sure to check the schedule as I'm not sure if the bus will get you to Grouse early enough for the Breakfast. I did just look but summer transit schedules aren't out yet. But it would be $2.75 each so very reasonable.
Cap suspension bridge is on route to Grouse and the 236 bus stops right there both ways. If you did it on your way back from Grouse it would be worth a stop. There's not a ton to do for the $40 price tag, but you're on vacation and the views are really gorgeous. Some stairs around especially on their clifftop adventure but the bridge itself only has a few stairs. I say go for it!
Your land sea tour would be neat too. I've been up the sea to sky gondola. Again gorgeous views and some easy trails to wander. (and some less-so easy trails if that's your thing!) Something to consider if you want to save time and money, you could rent a car from DT Vancouver and use it to do your own tour up Sea2Sky. I'm sure it's cheaper for the car rental plus attractions vs Land and Sea, and gives you the ability to take it to Granville Island before dropping the car back at the rental office that night. It's very easy to navigate Vancouver/sea2sky if you have Google maps on your phone with a data plan or any kind of GPS.
Granville Island is neat. It's not a must do, but it's worth doing if you can squeeze it in.
As far as rain goes, it can rain in Vancouver anytime! But in general July and August are 75-85 degrees and sunny. Again no guarantees but Vancouver is typically beautiful in the summer.
Think that covers all everything for now. I've lived in Vancouver for over 10 years and it really is a world class city.
Enjoy your trip and happy to answer any more questions you may have!