I want to level up my archery skill. If there aren't any archery targets would firing at a tree or sign work?

Try angi's Camp. Its south of Falkreath high up in the mountains. The path starts by peaks shade tower which is south east of Falkreath. Angi's camp should be perfect for your needs.

Very useful. Thank you.

There are targets in the Castle Dour yard in Solitude. I've seen them elsewhere too - though can't remember where offhand. Lots of places though....

The wiki article doesn't say this specifically, but like the spells that only count if they are used in combat I believe only arrows fired at stuff that can be "killed"
count towards your skill. Shooting at targets/trees won't work - although you will learn about the flight path differences at various ranges. Unless doctored,
(on the PC) arrows rise and then fall again depending on how far away the target is. And really distant stuff (say dragons flying around) doesn't get hit at all.
It's like the arrow either passes right through them or appears to hit, but actually falls away before it gets there.

Angies camp works for about six levels. Otherwise you can use trainers/companions.

Archery targets and practice dummies exist in most main cities, in Whiterun behind the Companions building, keep courtyard in Solitude, next to the keep in Riften (in the thieves guild training room too), probably in Markarth and Windhelm too somewhere.

I can't say whether they'd help level skills though, I've never tried and prefer live targets myself.

If you're rich you're honestly better off using trainers. If you have no reservations about using exploits, you can make use of Faendal up until Archery 50 by making him your follower, let him train you and take back your septims from him. Otherwise just play the game normall and do the random "go kill x in lair y" quests from the Champions. Other things you want to try is to get Shadowmere by going through Dark Brotherhood's quest, crank up the difficulty to Masters and wail on it with your arrows. Shadowmere can die in Skyrim, even though it has fast health regeneration.

Personally I just used trainers + do quests normally. The Shadowmere method gets boring really fast.

The companions as harbinger. Think Faendal only like x6

You can use that Huntress (Aela I think) from Companions too if you plan to do that questline. If so you can train up to 75 Archery for free.

Angies Camp, if you talk to Angie shell give you special arrows to practice with. Doing her little practice drills will give you about six levels.