Losing 20-25 lbs in 2.5 months is aggressive, especially if you are in the mid 100s already. I would just focus on doing your best and see where you get. I personally don't like weight goals. Activity goals (staying on plan, exercising, etc) are helpful though.
You don't have to go to the gym to exercise. You can walk, you can hike, you can jump rope, you can do exercise videos, etc. You can also do body weight exercises. You can do crunches, pushups, tricep dips, etc. You can also look into resistance bands which are a good, cheap, portable way to work out.
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