The city developed and expanded from the creek area towards the south-west over time. Even so, the only buildings older than 40-50 years are in the 'historical' area near the museum (Bastakiya, Al Fahidi). Nat Geo has some walking routes around the creek you can google for.

Dubai Marina is perfectly 'authentic' if you are a young white westerner who enjoys alcohol, fast food chain restaurants and night clubs ...

Half-way between is Downtown, with the Dubai Mall (aquarium, fountains, waterfall) and Burj Khalifa. A little further is Mall of the Emirates with indoor snow skiing.