I like this suggestion if the OP wants a gentle relaxing day. Mainz is also a pleasant and interesting small city.

The tower is closed due potential collapse

Oh looks like I have good hiking options if the weather is good. Some of those would be perfect for me.

During one of our stays in Germany we were staying at Neckargemund. From Neckargemund we hiked to Konigstuhl where you get great views over Heidelberg and there was a good little funicular museum. We rode 2 funicular down to the Heidelberg Castle area-you could spend a lot of time in the castle area (pharmacy museum & worlds largest wine barrel).
You can do a river cruise or bus trip from Heidelberg to Neckargemund-bus trip hugs the river. Good pub on the river at Neckargemund for drinks & a meal.
As per aysoo the walk to Neckarsteinach is a good hike.

By train the - absolute - minimum travel time Heidelberg to Freiburg is about 1h40 mins if you get the fastest train and always involves a transfer (usually at Karlsruhe or Mannheim).
IMHO going to Freiburg for a daytrip is stretching it a bit. Certainly doable but ...
I live a 10-15mins drive (depending on traffic) away from Heidelberg and with train travel in mind I�d rather consider Stuttgart, Karlsruhe or Speyer.

I would double this

If you're walking along the Nekar, which bank of the river is more foot travel friendly?

Karlsruhe.. been there found it fairly boring sorry Actually when I was in Karlsruhe I did a nice day trip to Heidelberg and another to Strassbourg. Is it that much faster to get to Speyer by train than Freiburg? I agree 1h40 is a bit much for my time budget.

If you take the S-Bahn to Speyer then it is either 43 or 49 minutes from Heidelberg Hbf to Speyer Hbf (Central Station). They seem to run every 30 minutes. For details, pls. have a look at https://www.bahn.de/i/view/USA/en/index.shtml

Thank you all for your time and helpful suggestions! My flight is tonight. Weather is throwing my desire for lots of walking for a bit of a loop - it's really really hot and as the weather people say, "record temps this week in a band from Stuttgart to Frankfurt and Berlin". So I'm going to adjust plans based on that maybe walk around Heidelberg in the early morning and then go to Speyer (most likely) or Stuttgart (if I want to be inside AC museum) in the afternoon. Going for a 5 or 6 hour walk in the heat isn't likely to make me happy.

But I've learned that there are nice walks in the hills on both sides of the Neckar in Heidelberg (e.g. Konigstuhl above the Schloss and the Heiligenberg on the side opposite the city) and maybe take up the suggestion of walking on the Neckar early and taking train back into town when it gets warm. I'm sure I'll do well and really appreciate the ideas here!

Sensible plan ...
But weather forecast is that starting midweek (from late wed/thu) temperatures will get lower to more comfortable levels (22-25�C)

So once again many thanks for all the advice! My free day is just about over so I thought I should wrap it up with a report.

Very hot today, high was 32 C I think. I got out early, went to the castle, then walked up the "Himmeleiter" - a stone staired path that just goes straight up - from there to the Konigsthul. There was a nice view from there but hazy. There seems to be a closed observation tower that would give 360 degree views from above the trees.

I just followed the Neckarsteig path, which is marked on trees and such with a stylized "N" mark and well marked. I kept going past the Konigstuhl as the trail follows ridge through nice forest (i.e. shade). Eventually I met up with a path which went back vis Felsenmer and using maps.me navigated around the castle back to my hotel, where I took a needed nap (9 mile walk). Had a few nice views over town and the Neckar but most of the walk was wooded.

Then I headed over to the Hauptbahnhof to catch a train to Speyer. They go twice an hour. I was just about to miss one when I passed a bus labelled "Speyer Domplatz" getting ready to pull out. I hopped on it. Now it turns out that bus takes a very circuitous route and I would have gotten to Speyer faster by waiting for the train, but the bus did go right to the cathedral, which saved me the walk from the train station, and I got to see a bunch of random small towns along the way.

Wandered around Speyer seeing the local sites (Trinity Church is closed for renovation, but I'd found that out ahead of time so was not disappointed) and took the train back to Heidelberg in time for a sunset walk along the Neckar.

Now I'm beat and ready to sit around all day at my conference tomorrow listening to talks. Again, thanks for all the great ideas, I am really impressed by the breadth of the Flyertalk community!

Nice you enjoyed it.
I should have told you before not to take the bus (route 717) ...
But you were obviously (and luckily) not in a rush.

Maybe it was a bit too much for the day ?
Are you sure you�re able to follow the conference without falling asleep ?

I think you got the best from your day. Glad you liked it. I hate conferences, but that�s also part of life