To many artists, a studio represents a place to retreat from the world, gather thoughts and make work.

For Glasgow-based Ally Wallace, the process of giving up his studio has been not only positive, it's been liberating - which is ironic, because buildings and their relationship to the people who live and work there form the lifeblood of Wallace's art.

He has form in this respect. Thousands of visitors and patients file past his coloured glazing at the New Victoria Hospital on Glasgow's south side every day. Soon the same thing will happen at Bristol's new Southmead Hospital, where he has made nine painted aluminium discs atop posts protruding from planting. They will be viewed through windows of upper floors.

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The turning point from doing studio-based work to becoming a roving artist-at-large came after Wallace spent time on a residency in Dusseldorf in 2011. "It was so exciting being out in city," he explains. "In 20-odd years of doing installation work, I realised I didn't make much work in a studio. Because it was so cold in Germany, I gave myself an hour to complete drawings and that has since become a pattern."

In the last few years, following a decision to let his studio space go, Wallace has made work in locations as diverse as Glasgow University's Bower Building, Summerlee Museum of Scottish Industrial Life, Scottish Opera's administrative HQ, RMJM Architects' Glasgow office and Martyr's School in the Townhead area of the city (designed by Charles Rennie Mackintosh and now housing Glasgow City Council's social work department).

Wallace has also spent time at the Lillie Art Gallery in Milngavie, a building he describes as being in possession of a "really odd roof". Purpose-built in 1962 by funds left by local banker and artist Robert Lillie, the gallery is probably best known for its connection to the painter Joan Eardley, whose family lived in the area.

"It's a really interesting place," says Wallace, who first visited the gallery to see an exhibition by Margot Sandeman, a close friend of Eardley's. I've been coming on-and-off since spring 2012. That summer, I did a lot of little pencil drawings. Since August 2013, I've been here every week.

"I realised after doing the drawings that the gallery had an amazing collection so I ended up coming in and looking at items from the collection in as much detail as the internal fixtures. It's very interesting for me to look at corners of places. There have been lots of 'bits' added to the gallery and it all came together to make a portrait of place."

The result has the effect of making this viewer recalibrate her vision of this working building. Visitors are more used to looking at work here in frames or plinths, but Wallace has take the sum of the gallery's parts, and then deconstructed them to create a whole new parallel Lillie.

Connected Parts begins when you walk into the first of two galleries given over to Wallace's work. In this squarish white space, with its distinctive low false ceiling and picture rail running, he has pinned his biggest pieces around the walls, including huge gaudily colourful painting studies of artworks he found in the collection.

The artist made these paintings on the floor of the gallery while it was open and visitors were talking to him. Works he has looked to for inspiration include paintings by Anne Redpath, Leon Morrocco and George Leslie Hunter. He also took out 3D pieces such as a vase and a bronze goose, and made work based on his impressions of them. All the paintings were made using ordinary household paint. There is also a 'still life' made from old pieces of cardboard he found in the gallery storeroom.

Wallace has placed two of the works on an installation made with wood salvaged from skips in the area. One reveals a rectangular painting in lime green with a circle cut out of the middle. While I was interviewing Wallace, veteran Scottish artist and writer Alasdair Gray happened to come into the gallery to drop off work for another exhibition. As he stood, framed by the circle, after a brief inspection of the work he pronounced it "most jolly".

Jolly the work in this room is, but step into the back gallery, with its livid red walls, and you discover a more introspective study of Lillie's overlooked corners. Wallace has pinned six or seven watercolours in here. They depict (very loosely) details from around the gallery such as a wooden bench, linoleum and the reception desk.

They are complemented by small pencil drawings of details such as sockets and door handles as well as cardboard cut-outs which, on closer inspection, turn out to be quick-fire stanley-knife drawings of the aforementioned cooky exterior of the Lillie. There are also a small balsa wood study for a sculpture, some working drawings in watercolour looking at how to design the space and pencil rubbings of little details such as a kick stool.

"If they were all separated, it would make no sense," says Wallace. "Some of the drawings are like ones you might see in schools made by sixth-year pupils. But I knew if you put them next to, say, linoleum then it would work as it would set them in context."

Nothing in this exhibition is left to chance, although regular visitors will have to work a little harder than usual to take it all in.

What Wallace has done is frame this hard-working local gallery in the most sympathetic of ways. There's nothing gilt-edged about it.

Connected Parts: An Installation by Ally Wallace, Lillie Art Gallery, Station Road, Milngavie (0141 956 5536) until March 20