Quite frankly the end of March is not a time of the year I would consider for a multi day hike in the Swiss Alps. Even in the lower parts of the country the weather can be quite unpredictable.
If you go in late August, September and early November I would recommend:
Day 1:
Davos Madrisa - Gargellen; stay overnight in Gargellen in Pension Wulfenia
http://www.wulfenia.co.at/
Day 2:
Gargellen - St. Antönierjoch - St. Antönien
take public transport to Linthal
stay in Linthal
Day 3:
take the Alpentaxi to Tierfehd
Cablecar from Linthal Tierfehd up to Chaltrittli
Hike to Muttseehütte
stay overnight in Muttseehütte (gets crowded on Weekends, go during the week)
http://www.sac-winterthur.ch/huetten/Muttsee.htm
Day 4:
hike across the Kistenpass to Brigels
stay in Brigels, Disentis or Sedrun
Day 5:
take public transport to the Oberalppass
hike up to Fellilücke
hike down the Fellital
stay overnight in the Treschütte
http://www.sac-albis.ch/huetten/treschhuette-sac/
Day 6
hike down to Gurtnellen (about three hours) and head off to wherever you want to go
These are all places out of the way of international tourists and will thus be cheaper than the usual tourist hotspots. You have to be fit and able to walk for 6 to 7 hours a day.
If you are looking for even more cozy and inexpensive places in the alps, here are a couple of additional suggestions:
Spitzmeilenhütte:
http://www.spitzmeilenhuette.ch/
This can be combined as follows:
Day 1:
- take the cablecar up to Flumserberg Maschgenkamm
- hike 2 hours to Spitzmeilenhütte
- stay overnight in Stitzmeilenhütte
Day 2:
- hike around the Spitzmeilen and down the Krauchtal to Matt (about 5 hours)
from there you could go on to:
Äugstenhütte
http://www.aeugstenhuette.ch/frameset.html
(either stay overnight if you arrive from Matt or just have a beer)
the new cablecar will not operate until about early July
hike across the Schwarzstöcki and down to Murgsee
stay overnight in Murgseehütte
http://www.murgsee.ch/murg_frm.html
and proceed the next day via
Murgseefurggel, Spaneggsee, Talalpsee to Filzbach
All places are accessible by public transport. You will not need a car. Hiking maps can be found here:
http://map.wanderland.ch/?lang=de&p&route=all