Ive lived here since 1995 and Ive never been to Grouse so I dont have any advice on that. I did just look it up and it looks interesting if you can see the bears. Not sure if it is guaranteed sightings or not. I may actually take a trip to see this summer. Its always struck me as pricey if you werent going there to either ski or do the Grouse Grind (hike up to the top).
I have been to Stanley Park and Granville Island many times though and in July with the beautiful summer weather I would spend the whole day at those two places.
One of the most popular things to do in Stanley Park is to walk and or bike the seawall. The entire seawall is about 21km long I think it takes 2-3 hours to walk the Stanley Park portion. You start at lost lagoon and make your way around the outside of the park.
In Stanley Park itself there is lots to do to keep all ages entertained.
At one end of the seawall is second beach which is a nice beach with concession stands, a playground, washrooms and lifeguards. Theres a floating dock that you can swim out to and dive off of. The celebration of lights fireworks can be seen from there they are July 27 and 31st in case those coincide with your dates. Its obviously not comparable to the Caribbean but its a nice place to swim in the Pacific ocean.
If the beach is not your thing there is also second beach outdoor pool right beside it. It can get crowded on super sunny days but my kids like to go there for an hour or so to cool off after walking the sea wall. The family rate is $2.67 a person so its pretty inexpensive even if youre only going for a short time.
On another section of the seawall is a waterpark with concession stands and picnic tables. Its also close to the miniature train and aquarium (more on them in a bit). A little further along is third beach (not sure why there isnt a first beach!) which is a little quieter then second beach but still nice. There are also concession stands and lifeguards there.
If you dont want to walk the seawall or if the less mobile members of your party arent up for it but still want to see the whole park then they can take one of the horse drawn carriage tours or the shuttle bus. The horse drawn carriage tours are an hour long from start to finish and they can take 20 passengers at a time. Its fully narrated and stops at the Totem Poles, the Girl in a Wet Suit Statue, the S.S. Empress of Japan Figurehead, and the Rose Garden. Its $31.99 for adults, $16.99 for children and $29.99 for youth and seniors. If you buy a combo ticket with the aquarium you save $5.00. They run every 20-30 min or so.
The trolley is a 45 minute narrated tour that stops at 15 different places in the park. The family rate is $22.32. Its a hop on, hop off kind of ride so you arent forced to stick to someone elses schedule. Once you buy your ticket you can get on or off at any of the stops so if you want to spend a lot of time at one place and not at another you can. It passes by each stop every half hour or so. Its not expensive $8.93 for adults, seniors and youth and $4.46 for child. I won tickets for this once but wasnt able to use them so I gave them to my parents and they loved it.
There is a mini train there as well that winds through one area of the park. In the fall it becomes a ghost train and in the winter a Christmas train. Ive done both (the Christmas one we do every year!) I havent done the summer one yet but I am going to this summer. It becomes a Spirit Catcher train and transform into Klahowya Village that showcases some of Vancouvers unique aboriginal culture. At the village there are artisans working you can watch, traditional story and legends at the Story Telling Circle, a 11:00 daily opening prayer and at 2:30 a smudging ceremony (not sure that that is). From June 29 July 2nd is Metis Nation Day and from July 27-29 its Squamish Nation days. A family pack for the train is $25.00 (up to 4 people). The entire site is wheelchair accessible and the train has a specially designed carriage that can seat up to two wheelchairs.
In Painters Circle, landscape artists display their paintings in an outdoor gallery. Closer to the aquarium, portrait artists draw pictures and caricatures. The do black and white or full colour and they usually do them pretty quick.
The aquarium in Stanley park is a nice size. Its not the best aquarium Ive ever been to but its quite nice. We have been a few times and the kids still ask to go. My youngest just recently did a sleepover there and slept beside the dolphins. I was jealous! Its sort of in the center of the park close to the mini train.
There are 4 restaurants at Stanley park The Teahouse, The Fish House, Prospect Point Café and Stanleys Park Bar & Grill. I have never eaten at any of them so dont have any reviews on them.
There are two gardens the Rose Garden and the Shakespeare Garden
Malkin Bowl (outdoor theatre) does Theatre Under the Stars which is lots of fun - the two shows for 2013 so far are Legally Blonde the musical and How To Succeed in Business without even Trying.

They also have outdoor concerts there fairly regularly I believe

The schedule should be released soon.
Fresh Air cinemas did free movies in Stanley Park in 2012 and Im sure they will again this summer but they haven't announced any dates yet. If you havent been to one before its kind of like a drive in without the car! Its a perfect way to end the day!
Thats it for Stanley Park I will work on Granville Island, Denman Street (where you can rent the bikes for Stanley Park) and dining next
