Being completely partial here, but I'm not ashamed of it.
Top of Easter Road: there are some already, and well used. More if possible at the top/south end, near London Road, as the shops are busy there.
Montrose Terrace: quite a few new shops and businesses there, and a lot of cyclists use this route east-west so hoops would encourage passing trade.
Cadzow Place: near Eastside Bikes. Currently some railings nearby, but a hoop would be better.
Portobello: lots of cyclists go there or pass through. Some hoops on the High Street would be handy for shops. There is some bike parking on the Prom but folk (including myself) seem to prefer railings. Don't know how feasible hoops would be there but at least they would be 'official'.
Leith Walk: lots of places here. This may be addressed by the redevelopment plans, but some hoops would be useful by the shops on the northern section of Elm Row, and outside shops, banks, etc. on the Walk north of the Brunswick Road/MacDonald Road junction.
Broughton Street: lots of shops, cafes, etc. here. Most folk lock to railings currently. A hoop in the vicinty of Real Foods perhaps?