Best to keep moving rather than staying in one base, so that you don't have to loop back on yourself. It's a lot of driving when touring Iceland because things are quite far apart. But it's easy driving on single carriageways through beautiful landscapes with no traffic jams, so an enjoyable experience.
I would allow two nights for Snæfellsnes, but in two different places. Maybe you could do the first night in Reykjavík, the next day drive the golden circle finishing with Þingvellir, stay near Borgarnes. Next day drive Snæfellsnes and stay on the other side near Stykkishólmur. Then you could go to the west fjords or head north towards Akureyri if that appeals more.
If you could afford a domestic flight the best way would be to end by flying back from Akureyri or Ísafjörður. Otherwise you have to count on driving back again and maybe end in Patreksfjörður or something? Just play around on Google maps.
Check out sundlaugar.is and find a natural hot spring. Hellulaug in the west fjords is amazing. Other things there are Látrabjarg (though the puffins may not have arrived yet, depending how early in May it is), Rauðisandur, Dynjandi.
If you go north, Dettifoss is absolutely jaw dropping.