As good an argument as any for the continued potency of the Christian faith - at least where artists are concerned - is the ability of churches to lend dignity, gravitas and profundity to art works displayed in them, whether those things are present in the pieces or not.

Craig Coulthard's half-hour film The Drummer And The Drone, an Edinburgh Art Festival (EAF) commission, can stand on its own merits wherever he cares to show it. But its exhibition in the cold, dark, echoing airiness of the Trinity Apse, located just off the High Street and one of the most atmospheric of EAF's off-site spaces, certainly enhances and intensifies its very particular flavours.

It's a neat marriage too, as the work is presented as a futuristic memorial service for a series of unmanned aerial vehicles (UAVs) which have been used in a variety of situations. These UAVs are more popularly referred to as drones, of course.

One of these, we learn from the female narrator, has helped track the last Scottish wildcat. Another distinguished itself tackling typhoid in Italy after a volcanic eruption. A third dealt with a hostage situation at a research station in the Antarctic while also "eliminating" the hostage-takers. Already vaguely apocalyptic sounding, that's where it starts to get creepy.

Meanwhile we see footage of a piper and a drummer playing a series of British army standards, such as Barren Rocks Of Aden, The Heights Of Dargai and Flowers Of The Forest. So here's another kind of drone. Finally, Coulthard's camera moves along a track before rising to show a wooded hillside, a loch and, in the distance, the loading facility for the UK's Trident missiles - though you won't know that unless you read the accompanying handout.

Unless you're the most extreme sort of Doctor Who fan, a police box won't carry the same sense of awe as a church, and that's especially true of the one halfway down Easter Road in which Edinburgh-based artist-musician Yann Seznec presents Currents, another EAF commission.

Seznec's work isn't without wit - his 2013 piece Twitter Bells was made from Meccano and bells, and rang every time someone tweeted using a particular hashtag - and for EAF he adds weather to the mix too: his piece connects fans from decommisioned computers to the internet and allows them to blow in relation to the real-time windspeeds in (variously) Newfoundland, China, Edinburgh and Thailand. With the door closed, it's mostly a sonic experience, enlivened by the odd flashing light on a sort of plywood dashboard he has constructed. Come to think of it, that is kind of like Doctor Who's Tardis.

Also on Easter Road is An Attempt At Exhausting A Place (In Edinburgh), one of the wordiest titles in the Art Festival and the one which perhaps required the greatest endurance on the part of the artist - at least if you think spending a week in a cafe earwigging on people's conversations is hard work.

The artist in question is filmmaker Alice Finbow, who's updating an idea French writer George Perec had and which he turned into a book in 1974 called An Attempt At Exhausting A Place In Paris. He did three days in a cafe; Finbow's doing seven and is on day five when the Sunday Herald drops in for a chat with her at her window seat in the Manna House Bakery. The results of her efforts - a series of A3 drawings and charts - are now posted on the wall there.

Rhubaba is an artist-run exhibition and studio space tucked away between two mechanics' workshops on Arthur Street, just off Leith Walk. Here you can see Diorama, a two-monitor video work by Augusto Corrieri in collaboration with Vincent Gambini, a conjuror and magician who's doing what's being termed "a residence".

Diorama shows a sheep on a stage and a man in a field, with both films being screened simultaneously side by side. It takes a while to work out what's going on but when the penny drops it's pleasing, if not particularly deep. Ah, but there's a twist here which hints at something else going on below the surface. I won't spoil it except to say that Corrieri and Gambini have a lot more in common than just an Italian surname.

Another co-operative affair is Captain Lightfoot, the group name of Edinburgh College of Art graduates Anneli Holmstrom, Emma Pratt and Kadie Salmon. Along with invited artists Jessie Makinson and Stephen Kavanagh, they mounted Captain Lightfoot Presents ... in the Glasshouse at Lauriston Castle. This small-scale exhibition of work (its run now ended) responded to the castle, a 16th-century tower house with 19th-century add-ons, and its grounds, which look towards the Forth and the Cramond foreshore.

The 16th century also has a place in Jacqueline Donachie's EAF commission, Mary And Elizabeth. The women in question are Mary, Queen of Scots, and her cousin, Elizabeth I of England, and the piece consists of two sculptures, one named for each of them and situated in West and East Princes Street Gardens respectively.

Blood red is the order of the day here, both for the sculptural piece (Elizabeth) and for the interior of Alexander Garden Forgie's rather splendid (and listed) shelters. As well as the paint job, Donachie has fixed the name Mary on to the roof of the middle of the three shelters, and the two pieces sit separated by the train line connecting Edinburgh with London.

Using an adapated bicycle, Donachie has drawn a red chalk line from Cockenzie to the city centre. It's intended to fade and a combination of rain and feet has done a pretty good job. History and politics, then, are Donachie's concerns - Mary And Elizabeth offers no particular comment on either, but it foregrounds the question of Scotland's relationship with England in a pleasing enough way.

Edinburgh Art Festival runs until August 31, www.edinburghartfestival.com