If your itinerary stays as is you have to forget about Mongui. We went to Mongui before Villa de Leyva. We took a bus from Bogota to Sogamoso and then a bus to Mongui. From Villa de Leyva you will have to go to Tunja first, then Sogamoso and Mongui. And then back to Sogamoso and Tunja for San Gil and then Barichara.
I think it would take at least 3 hours from Villa de Leyva to Mongui and then once you are back in Tunja it would be 4.5 hours to San Gil, change bus stations and another 45 minutes to Barichara. So you would hardly have any time in Mongui. Skip it. Traveling there and then to Barichara takes too much time. Mongui is beautiful but Villa de Leyva is great too and I liked Barichara the best of all the towns we saw. Also, a big attraction for me in Mongui was the Paramo de Oceta hike but you need a day for that.
Villa de Leyva: apart from wandering through the town we also hiked up to El Santo early in the morning for a nice view. And we walked via Casa Terracota and El Infiernito to the Centro de Investigaciones Paleontologicas and loved it (the English tour was great) and El Fosil. We also hiked to Laguna de Iguaque, tough hike to a beautiful spot. I recommend you do that hike for sure as it is your chance to see the paramo (the frailejones are amazing). There were other hikes possible in the area. There is also a monastery but we didn't go there.
Barichara is beautiful. Great views as well. Don't miss the ecopark behind the Santa Barbara church. And check out the cemetery.
When you go from San Gil to Bucaramanga you can check out the Chicamocha Canyon. We wanted to go but the only day we had we were informed the road was closed because of a bicycle race...
Salento: it is a nice town. There is a viewpoint. There are coffee farms where you can take a coffee tour. There is the Kasaguadua natural reserve (an interesting project... two men are working to return former livestock pastures back to cloud forest.). And of course the Cocora valley where you can do a short hike or a long hike (I recommend the latter and go to Acaime as well to see the hummingbirds). Two days there is enough: one for Salento, Kasaguadua (if of interest) and a coffee tour. One for the Cocora Valley. But maybe this is where you will go horseback riding and then that could be day 3.
Sunday is a good day for Manizales. Try to see one park (we went to Los Alcazares for a hike and to see birds but there is also Recinto del Pensamiento).
There is also the cathedral and the Chipre viewpoint (and the Monumento a los Colonizadores) for the sunset. On Sunday the locals go there and it was a lot of fun. Great atmosphere. Good street food too. We also enjoyed the cable car.
You can't go to Jardin and Jerico in one day. You need at least a full day for Jardin and you first have to get from Manizales to Jardin. That can be an adventure. From Manizales you can take a bus to Riosucio. But make sure you are there in time for the bus to Jardin. We went from Jardin to Manizales: the bus to Riosucio was a chiva for part of the way... quite the experience, very narrow unpaved road and amazing views (3 hours). In Riosucio we took a bus to Manizales (2 hours).
Jardin: it is a beautiful town. A few nice hiking trails (look for birds) and you can go back to the village by cable car (don't miss the wooden one!). When we were there in February the waterfall in the cave (La Cueva del Esplendor) was closed for maintenance (not sure for how long) so that was unfortunate (you can hike or go by horse). We went to the cock-of-the-rock preserve (beautiful birds). We were there on a Saturday and loved watching the cowboys come into town in the evening with their trained horses. The tourist office in Jardin is quite helpful and will give you a map and tell you about hikes, things to do, buses...
As a day trip from Medellin we chose El Penol and Guatape. Never made it to Santa Fe.
So you chose La Guajira. Let me know how you like it. Another destination I kept reading about but could not get convinced about. As you know, I chose Tayrona (and Minca) instead.
Are you into salsa? Otherwise I would not worry about Cali. I have not been (well, we were there but only because our bus stopped there briefly) but I keep hearing it is just not that interesting.
I see no need for a car. In Salento we walked a lot and jeeps go everywhere as well (Cocora Valley...). Then take a bus to Pereira and a bus to Manizales. In Manizales we walked and took taxis. And the cable car.