Verona Day Trip

The Giardino Giusti (a beautiful Renaissance garden admired by Mozart, Goethe, Tsar Alexander, etc.) has a Belvedere (literally, ‘beautiful view’) from which you can overlook the city.
Should mention that it’s a pretty substantial walk from the train station just to the Piazza Bra, and another to the Giardino Giusti, so since your time is so limited, you might want to take a taxi to the Giardino Giusti, then walk back down.

Hello movexz,

Depending on how much you want to walk and how much time you have I would take a taxi from the train station to either Porto Nuova (the Roman Gate to the old Town) or to Piazza San Zeno. San Zeno is slightly further way but will give you a broader look at the city.
From San Zeno check out the Basilica di San Zeno Maggiore which interesting and the wander the San Zeno neighborhood to the edge of the river and follow that around to Castelvecchio and take the pedestrian bridge Ponte Scaligero out over the river. From there take via Roma to Piazza Bra and join up with the Porto Nuova walk.

The Roman Arena dominates Piazza Bra and is a great place to wander. From there just keep following the city through to the loverly Piazza delle Erbe - lively with booths of food and the usual tourist stuff - and on towards Ponte Pietra. Cross the historic bridge - the white water under the bridge is the remnants of the old bridge bombed in WWII - and walk up towards the Funicolare di Castel San Pietro to reach the castle. That will give you views of the city and curve in the river.

If you really want my advice though what I would do is not go to the castle but instead turn right and go to the Teatro Romano and tour the excellent Museo Archeologico al Teatro Romano. It is the old Roman Theater (still used) the Archeological Museum - Roman and pre-Roman - along with an old convent attached to the site. If you walk all the way up the views are virtually the same as those from the castle but I find the ruins and museum much more interesting.

Don't sweat where you're going too much just wander the city and it will lead you to the various piazzas anyway. There was a famous photography museum that was in the Roman ruins but last I heard it had not reopened post lockdown. I'm hoping it will be open again when I visit in October.

Verona is super charming - have a great visit,
=Tod

The lookout point I think you are referring is across the river way up high on the hill
Probably too far as a stopover

The views from Ponte Pietra are pretty nice
I’d suggest taking a cab there then walking back thru P Erbe to P Bra
Then a cab back to station

Ponte Pietra is right at the river bend so you won’t see all of the town

As a follow up to ChristineH's point both of the walks I described are relatively long.

From San Zeno it's probably about 3km - just under 2 miles - and from Porta Nuova Roman gate about 1.7km which is just over a mile. (Just to be clear I was saying take a taxi to I Portoni della Brà - the old Roman gate on Corso Porto Nuova on the edge of the old city.) Adding to this distance getting lost, wandering to look at something interesting I would assume 2.5 or 1.5 miles respectively. I tend to walk a lot when exploring places on vacation so to me spending a couple of hours exploring like this is my idea of a good time and Verona is a great city for this, but obviously your mileage may vary.

Mass transit is pretty limited within the old city since buses run around the center rather than through it. There is one taxi stand right in the middle of the old town just off Piazza Erbe so while you can get a taxi to about anywhere picking one up when you're tired is more of a challenge. If the view was a main point you could get a taxi to near the funicular - that would probably be about 10e - ride up and get an over view of the city and then walk as much of it as you found interesting.

Needless to say I really like Verona and find the old town super charming and encourage you to take a few hours to wander it and see if you get charmed as well.
=Tod