I would say you'd have a bit of an advantage for availability and convenience if you stayed in West Hollywood, or even Hollywood, or midWilshire, or Beverly Hills, etc
Plenty of providers would travel to downtown, no problem - but LA traffic always rears its ugly head and you will definitely have more flexibility if you're not in downtown. I tend to say I won't even consider driving downtown between 7-10am and 4-7pm.
Not sure how you want to balance convenience for your work - the flip side of this is that you may not want to fight the traffic yourself for work.
Will you have a car of your own and be willing to travel?
Will you want to walk to shops, restaurants, etc on weekends and evenings? Downtown is much more active than it was 10-15 years ago, but you still can't compare it to the nightlife/street scene of West Hollywood.
Bottom line - you will have no problem getting a great provider to come downtown, but you probably increase your selection of guys and time slots if you're not downtown.