So where are the old buildings, museums and theatres? Diera & Souk Al Kabir area and the Al Shindagha area. That's not even mentioning the awesome ones in Sharjah which aren't far away.
As for theatres, there are ones that show traditional dancing, but there's also Dubai Opera and Le Pearle for more modern Broadway, Cirque De Soleil type stuff.
Or the array of wildlife you see in Southern Africa? Well the UAE isn't South Africa so the selection of wildlife isn't as robust, but you can see wild gazelle, oryx, donkey's, camels, fox, Khubara, falcons and for some reason Patagonia mara, and other desert wildlife in abundance at Qudra Lakes and you don't even need to hire a safari guide. Locals say that there are still wolves and leopards in the mountains, but you'll be awfully lucky to see those!
Or the colourful street life in India? Obviously this changes in the summers, but in the winters most of the souks are teaming with festivals and there's celebrations in the various parks around the city. There's even an area called Global Village which invites expats and locals to set up stalls to showcase cultural wares and foods. You have to remember that Dubai is very multi-cultural, so depending which area you go, there will be different street life. DragonMart area is basically China Town.
Gardens and temples such as you can see in Japan? I think not.
Miracle Gardens, the umpteen parks around the city. As for temples, while the most beautiful mosque in the world is in Abu Dhabi (Shiekh Zayed Mosque), all mosques are open to the public outside of prayer times, there are old ones, new ones, modern ones, conservative ones. There are some churches and temples in the city, but they're fairly modern so not as beautiful or interesting as some of the older mosques in Shindagha.
All of this stuff is here, and easily accessible if people stopped feeding into the stereotype that Dubai doesn't have this.
And FYI, this is just Dubai, the rest of the country (and it's not a massive country) has even more to offer in terms of history including archeological sites of 10th century Monastery's, areas with wild giraffe, cheetah, zebra and ostrich that have been re-introduced, and the most amazing mountains and wadi's you'll ever see.