These are all good neighborhoods. Personally I sell more 78704 than anything else, as the neighborhood is so close in and the lots are a decent size, clients seem to gravitate to this area. So if your planing to buy or sell for the short term or long term I would suggest 78704. The are has seen some very solid and consistant escalation in property values.
The other two neighborhoods are also good choices, however some parts of Hyde Park are difficult to sell due to the high level of student occupancy, and the houses are often much smaller and older (some as petite at 700SF) and the close proxemity to I-35 (free-way noise).
Some parts of 78723 have really large lots bigger than a quarter acre with trees, which appeal to many buyers. However you should check out the schools before you buy a home. Even if you don't have children, when you try to sell your home it may become an issue. I suggest you go to http://www.SchoolMatters.com
and look up Reagan HS and compare it to other Austin schools.
It sounds like it has been several days since you spoke to your agent. I would try calling his office/Broker and find out if something happend to him. If your agent still won't call you back, you may always cancel the Buyers Representation Agreement and obtain a new Realtor. I would read your Buyers Rep and see the details on termination. Your agent works for you and if he is not cutting the mustard, I know that you can find one who will. I wish you luck!
If there is anything I can do for you please don't hesitate to call me, 512-771-6318.
Good luck with your relocation!