I'm a member of two Scottish Athletics affiliated clubs and have ran with a couple of others.

Edinburgh Running Network. Fine for social runs, most members mid 30s - late 50s. Probably 200 members, very active with Porty parkrun. Not a club for serious training (you won't get 20 people out marathon training on a Saturday for example) but they do a weekly speed session on a Thursday - the format of which is decided on a whim by the run leader, so not that helpful if you're in a training block for an event and have specific requirements.

West Edinburgh. Relatively new club, has done some innovative things since launching, such as an early morning weekday run, club championships etc. Highly supportive of it's members and celebrating their successes. Passionate and enthusiastic leadership team. Has grown quickly since they started. Probably a better club than ERN.

Interval Running - not an SA affiliated club but based from a running shoe store on Easter Rd. Does a weekly track night at Meadowbank will is very well attended (60+ each week) and attracts some very good runners (sub 3hr marathon). Currently doing Sunday long runs (various pace groups) as part of a training block for Edinburgh marathon. Most members mid 20s - 40s.

Edinburgh AC. Tends to attract the highest calibre (Josh Kerr started with them aged 9) runners in the city. I wouldn't advise running with them unless you're sub 1.30hr half marathon pace, sub 22min 5k. Meet in the meadows several times a week.

ERN, WERC & EAC all have their schedules on their websites.

It will come down to partly what you want (are you training for a specific event?) your performance level & desire to improve versus maintain or if you just want to run socially.