I am moving to Dubai by next week and am currently looking for a small studio for residence with a budget around AED 50k per year…I will be working on Sheikh Zayed Road next to Mall of the Emirates so looking within this zone . Please advise me what neighborhoods I should look into within this budget to be with walking distance or access to public transport.

I would recommend you look in Barsha and Tecom areas.  Both have access to buses and metro Barsha depending on the building you choose maybe in walking distance to your office.