It'll be safe but crowded as fuck

I live in Somerville ~0.5 mile from Porter, ~1 mile from Harvard, ~1 mile from Davis and my fiancee and I pay $2250/month in total (so $1125 each) for a smallish 2 bedroom. We had to pay a half month's rent as broker fee + first month's rent + last month's rent when we moved in ($5500 total up front -- our rent was slightly cheaper the first year) but had no security deposit.

If you're willing to forgo certain amenities (like central air, in-unit laundry, private balcony or yard) that are generally only available in newer or more expensive buildings, you can easily find a place of your own within a mile of Harvard for under $2500/month.

If you're willing to live with roommates, you can find a 3-4 bedroom apartment full of grad students where your share is under $2k/month and probably under $1500/mo. Plus if you're taking over someone else's lease (like if most of the roommates stay, but you take over the lease for one of them), you probably won't have to pay broker fee or first month + last month upfront.

Rent goes up as you get closer to the T, and Cambridge is generally slightly more expensive than Somerville. But you can definitely find a place that's easily bikable or walkable to most of Cambridge and Somerville for much cheaper than what your friends are paying.