Inner Hebrides or Outer Hebrides

My choice would probably always be the Outer Hebrides, just because the islands are much less crowded than the Inner Hebrides. I haven't been to much of it, but what I've been to was pretty wonderful.

Of course, there's a lot to be said for Skye and Mull and other islands in the Inner Hebrides. Mull is much less crowded than Skye, and it's one of my favorite places, although I did love Skye. But ultimately, for me, the crowds are what control a lot of my destinations. Cities are one thing, but when I'm heading outside of the city, I don't like to be fighting my way through lots of people. One place that I loved that very few people get to is the Isle of Raasay, a 20 minute ferry ride from Skye, which has some wonderful hikes and a very peaceful and serene quality.

That said, it's unclear to me how long you plan on spending in either the Inner or Outer Hebrides. If it's just a couple of days, I don't think it would be worth it, but that's me. I think you really need to be there for at least four nights to really gain an appreciation for any of those destinations.

I'm assuming from your comment that you won't have a car. The bus timetable from Glasgow to Fort Willaim and onto Uig is here.
https://www.citylink.co.uk/media/p35hur1o/glasgow-uig-web.pdf

Bus services on Skye aren't brilliant. Portree to Skye Museum of Island Life here. (This is the winter timetable and summer may not be much more frequent. Also watch out for schoolday only services...)

Portree to Dunvegan Castle here. (I must admit I wasn't impressed by the inside of Dunvegan Castle,]. The gardens were OK.)

Oban is only about 3 hours on the train and is a frequent service. There's also more scope of things to do. Dunoillie Castle is just a short bus ride. Catch a ferry to Lismore from Oban.

Use West Coast motors for a day trip to Iona and Staffa... Alternatively catch the ferry to Mull and spend a few days there. I actually prefer Mull to Skye. There is Duart Castle and Tobermory has a distillery and is an attractive wee place.

Slightly pedantic, but both Mull and Skye are Inner Hebrides. Outer Hebrides are Lewis & Harris, the Uists, Benbecula, Eriskay, Barra.

Sightseeing Skye by bus requires careful planning and will be pretty restrictive. You don't say how many days/nights you'd be spending so hard to judge if it would be worth it for you.

If you wanted to see the Outer Hebrides then you could fly into Stornoway from Glasgow, then use the Spine Road Bus Service as it's known, all the way down from Stornoway to Barra; followed by the ferry or flight back from Barra to Oban (ferry)/Glasgow (flight).
Alternatively it is possible to take the train from the Lake District to Inverness arrive 1325, for the 1510 bus to Ullapool and the evening ferry to Stornoway.
Where I am in the Lake District, if I kick myself out of bed early enough I can actually be in Inverness by 1206.

The Spine Road bus service is pretty good, with integrated connections with the two ferries (Leverburgh to Bernera and Eriskay to Barra) en route- it would be a shame to do so, but the whole route can be done in a single long day. Maybe the only bus route in the UK to serve 8 ferry ports.

If you want one of those once in a lifetime type experiences, you could fly in and out of Barra, which has the only commercially scheduled flights landing on a beach. The flights take off from Glasgow. On Barra there are taxis, a rental car agency and a bus service that essentially runs on the school schedule. When we were there in 2019 the Isle of Barra Hotel had e-bikes for rent which we used as our transportation on the island. It looks like there is a bike rental shop in Castlebay, the primary town on Barra. Our main reason for going to Barra was the beach landing but also because my husband's family was cleared from Barra.

Without a car, Skye can be difficult to explore.

Traveling between Oban and Glasgow you can go by train one way and bus the other way taking different scenic routes. And with the bus you could include a stop over in Inveraray to see the castle and gardens or the town of Luss on Loch Lomond.

You could also take one or multi day tours to these areas.

I took the three day tour to Lewis and Harris this past September offered by Rabbies.

We went everywhere since the vehicle was a 16 passenger van. You will cover a lot more ground than trying to do it with public transportation.

I've done other tours with them and plan to do more.

In 2022 we visited The Outer Hebrides: Ferry from Oban to Barra, busses from place to place, ending in Stornoway and ferry to Ullapool. Very easy transport wise.

We had all accommodation booked before we left. I cannot see when you travel, but from May to September I wouldn't go without accommodation booked.

After seeing the plane land on Barra, I have dreamed of trying that trip. May never happen :-(