Now back to the question. I always take the Ben White Service Road to
Lamar and head north using Lamar till I get to the Pfluger bridge at
Riverside.

Map

I'm comfortable going at a decent clip with traffic on South Lamar
descending to the river. As they say, "Your mileage may vary." I only
use Lamar going downhill (north) where it's possible to haul buns downhill.

If you're looking for a more serene route (with shade too), continue
past Lamar on the service road crossing Ben White at Banister. Take a
left (North) onto Garden Villa which eventually leads you to South 5th
which you can take all the way to Barton Springs Road.

When returning up hill back to Oak Hill, I always use this South 5th,
Garden Villa, Banister route.

And since serene is the operative concept, it's possible to avoid Ben
White altogether if you take Jones Road, there's a connecting street
from the strip mall area on Brodie at Ben White that goes behind Burger
Center to Westgate and then you hop over to the the street behind
Central Market taking that to Banister, crossing Ben White (as above)
and continue the Garden Villa, South 5th & so forth.

Map

That said, I usually just take the more direct route, the feeder road on
Ben White, rather than Jones Road.

All sorts of ways to get to downtown from the town lake. I'll leave that
to you...

http://tinyurl.com/7l3j7

http://tinyurl.com/lnltu

I often follow something that incorporates Scenic Blvd,
Exposition, Mt Bonnell, and I usually make it a point to stop at
Central Market or Whole Foods as a destination or pit stop or to pick
up a few goodies.
http://tinyurl.com/czla8
(you'll need to use Mozilla, Firefox or Safari cuz this page link
breaks in Explorer) -- The blue path is the general route, but no need
to stick with it.

If you are asking about points farther South and West:
There are some nice places (and challenging hills) further south &
west like Lost Creek Blvd and Barton Creek Blvd but they involve
connections on Beecave Road and Loop 360 which I've grown to hate
because of all the cars. If you're up to that sort of route then you
might be interested in West Lake Blvd, Red Bud, Toro Canyon etc.

I don't understand the current obsession cyclists have with 620, SW Parkway, 360, etc. I guess my idea of a great relaxing ride isn't a wide shoulder with cars and trucks whizzing by. I greatly prefer East Austin - heading out toward Decker Lake or out Burleson Rd. back behind Bergstrom Airport. Less shoulder, but also less traffic and a heck of lot better scenery than strip-malls McMansions. And I've found the motorists much friendlier out East than west. I've NEVER ridden 1826 without some sort of "incident" - the worst being a beer bottle thrown at me, the very least some "kind words." I still cycle out there but only when I'm meeting other folks that insist. Further South seems even worse. I think you're required to hate bikes for Public Office in Williamson County.

You can cross from the West part of town to Burleson via Woodward. From the north (and thanks to several here for helping me with this route) take 51st Street out eventually getting on Loyola and Decker Lake Rd. After that it's quiet, clean, and open roads as far as you want to go. You can actually hear a vehicle coming up on you a quarter mile in advance. I've never had a bad incident out there.