I have a different opinion. You do not need one pack, you need two. Choosing one pack will leave you with a pack too big/heavy for a day hike, but too small to hold everything for a 10 day trip. (If I read your post correctly you want to use this as your sole luggage item for travels, carry-on probably).
However! I also noticed your price range is below $100, so we have to choose carefully..
I would recommend the REI Flash ($25,17 liters,281 grams) as the day-hiker, AND a Golite Jam ($60,38L,600g). Total cost $85. These are both quality packs with a good reputation here at BPL. You can pack the Flash in the Jam for the trip, then leave the Jam and most your travel goods in the hotel and carry the Flash on your day-excursions.
Here's the $59.45 Jam.
If you want mesh pockets and a lid on your day pack, consider the Patagonia Lightweight Travel Pack, ($60,20L,281g)
Or the Montbell Versalite 20, ($60,20L,350g)
You can stuff either of these into their own lid, then toss it in your Jam. I own the Versalite as my day-hiker, and prefer having the mesh pocket and lid for some of my "10 essentials".