Public transport is mostly just buses, the locals cycle. Bus tickets are not transferable, you buy a separate one for each bus ride, each costs €1.40. In season, there are oranges everywhere, on every street, dripping off the trees, however they aren't good for eating.
- There are some parks up in the north, on both sides of the river.
- You can try Alamillo park near the river, I was alone with tent and can say that it's a quite good place. [Update] Actually you can even find a beautiful cob yurt at this park where you could stay every day but Saturdays and Sundays. Just please bear in mind that this is an archeological project focused on educating children, so be very respectful and try to leave the place even better than you found it. Its location at the park:
The problem with park Alamillo as well as with most of parks in Sevilla is that it has it's closing time (in the summer it's open from 7 am till 2 am), so even if the guards won't throw you out of there before closing, keep in mind that you will be locked in the park for some hours (the fence is not easy to climb, maybe you can find a place to sneak in and out though if you search). The yurt is damaged now, there's been a fire or smth, and the whole archeological exposition place seems abandoned (08.2017).
There is a pretty good, a bit abandoned park near the center (Parque Vega de Triana). It's open all the time. At least in the north end of it you can find big bench like structures that are good to sleep on and if you put your ten there at night I don't think someone will bother you, just don't keep it there in the daytime (in other hand, thare are people living in tent's near Cristo de la Expiracion bridge all the time and police doesn't seem to care [09.2017]). At night there's no one there and in the morning there are people running, cycling, walking their dogs, no one hanging out with the beer or smth, so it's rather peaceful atmosphere for sleeping travellers.
Also if you're thinking about sleeping in parks on the grass (and this is for whole Spain wherever the grass is green) be aware that there are water sprays that are turned on automatically every few hours and it's very annoying.
Plaza de armas bus station is open 24 hours (I suppose as most of them in Spain do). Not sure how sleeping on the floor would work out there, but there's a free wifi there and it's a good shelter in case of rain or smth else. There's another bus station in southern part of the city center.
The "green river" (I can't find the original name of the water body, but it seems to actually be more of an artificial pond than a river) of Sevilla (the main one that runs thru the center) is good to take a swim. The water seems to be clean enough. There are pretty much of small piers along it that are comfortable for that. If you want more privacy you can find spots in park Alamillo. Rio Guadalquivir is very muddy.
There is a good dumpster diving spot at the Ponce de León square, where you will find the M.A.S. supermarket with a couple of small dumpsters. I'd also try the Supersols.
Every Wednesday at 14:00 at the Pumarejo square there is a free lunch organized by the "Mujeres Supervivientes" association in the big neighbours house, an association which fights against gender violence. You can contribute with donations. Currently (03.03.16) they awaiting for government benefits which would allow them to serve lunch three times per week. But this is Spain and everything takes ages.
Tourist office at the San Francisco square offers 1 hour of Internet for free. You just have to sign up on the desk there. Working times: 10-14h and 17-20h.
There's a free wifi in Plaza de armas bus staion (info hangs on the information kiosk [09.2017]). In front of any Mcdonalds and Starbucks. In some of the tourist offices.
My advice for whole Spain: go for the terraces! Don't be shy. Specially in Triana there seems to be less competition. The whole oldtown is good for busking, cause there are lots of walking streets more and less busy, just pick your spot.
The outmost worthwhile spot in Sevilla is El Huerto del Rey Moro. Located in Enladrillada street, in the very city oldtown, it is a beautiful squated city garden (actually the only one I know in Spain) run by the same neighbours and volunteers. There you can learn about permaculture with Luciano, a recognized expert in Europe, jam along with various musicians, meet families from the area, learn how to bake bread or make your own pasta, learn about bio-construction or how to make compost... Just the best place you can imagine, constantly visited by artists, free thinkers and, in general, people aiming towards new ways of living, who volunteer there and are slowly making this place some sort of a second home. Since three or four weeks ago (being today 03.03.16) they started organizing self-made lunches for the volunteers and other people involved in the garden. Anyone is welcome to participate in this wonderful project. Clearly the greatest one currently ongoing in this city.