In Peru, the area I liked the most were the east ranges of the andes. Everything between ~500m and 2000m elevation has amazing nature, but not as hot, wet and full of mosquitos as the lowland jungle.
The highlands are great areas for hiking, if you are into it. I've been in Huaraz for some time. You can go into amazing mountain landscapes there.
Concerning psychedelics, the easiest thing to do is brewing san pedro yourself. You can find them in almost all markets, or go out into the mountains and collect them yourself.
For ayahuasca, you don't have to necessarily go to Iquitos. the ayahuasca tourism there is pretty big and you need abit of luck, the get in contact with some good people, who are legitly into healing work and not up to rip gringos off.
You can find them, but you need to spend some time when you find someone it's also good to stay for a longer time and make a plant diet to really have a beneficial and healing experience.
The longer plant diets connected with regular ayahuasca ceremonies are much deeper and stronger than just doing a few ceremonies. But you need a little more dedication for this.
If you get the chance, try Kambo. It's a very beneficial medicine.
The city itself is not that interesting.
A nice market in belen (if you are there, get some mapacho tabacco for ceremonies, it's very hard to get it in this quality in the rest of peru);
the boulevard at the river, full of jungle tour agencies, restaurant, bars and cafes for gringos;
around the city there are some things like wildlife rescue centers a butterfly farm etc.
The rest of the city is just vast urban areas, more or less slummy, depending on where you are.
If it's only for the ayahuasca, you can find some curanderos in other parts of the country too and don't really have to do this trip...
A flight from lima is a little less than 100$. you can also go there by ship. It's about a week from Pucallpa and about 3 days from Yurimaguas.
Pucallpa should be possible with a bus from lima in a day AFAIK, Yurimaguas is a little further, but you can visit great places on the way. Cajamarca, Chachapoyas, Tarapoto... There are opportunities for hiking, camping, archeological sites, lagoons, highlandforests... all kind of things. And the north is by far not as touristy as other areas.
Pucallpa is a pretty big jungle city. But you can try to get to some smaller village and find a curandero working with ayahuasca there too. Many Shipibo live in Pucallpa.
I can't say much about Cuzco, the sacred valley etc.
If you have any more questions about anything, just ask