I'm currently in f2p. I've been training between 7 and nearly 80. I'm quitting at age 80 in order to improve my skills. However, I will likely join in OSRS Gold the near future. I would like to get a skill cape. If I get an ability cape, I don't need to cook or fletch just because it is very easy I want my first 99 to be special therefore I thought strength would be pretty decent. How long would it take to get 80-99 str? And which place should you train? It depends on the location you train in and how eager you are to pay to buy good food and cookware and so on.
In the beginning, I'll mention - the strength skillcape is nearly as popular as the fletching/cooking capes of today. For a truly distinctive cape, choose to go for mining, slaying and runecrafting. If you are willing to work hard, these skills can be learned easily and cheaply.
However, back to your original question, where to train the strength. Here are a few locations I'll mention pest control. It's a well-liked option, but it's not my favorite. Due to the relatively new pest control system it's not really as fast and won't earn you any hitpoints xp, and will be boring and sometimes frustrating. I would guess that you would play about 3-4 hours a day and spend 8-10 week training to be an effective pest control expert.
Massive skeletons are found in Damis' Lair. This is my favourite training spot. It is only possible to have guthans available to Old School RuneScape Gold increase the effectiveness of your training. This is where you can learn how to use a salve ammy. It gives you an additional +15% attack, and the ability to kill undead. It's a long hike to the bank so the guthans are important. If you're not looking to invest money, you can train here. This is slightly quicker than pest control, and more so if you own super pots. It could take 7 to 8 weeks here.