The Hilton Garden Inn at T2 & T3 Heathrow is lilterally connected to T2. It's less than a five minute walk to the Departure area. The buffet breakfast is very nice. I believe it starts at 6 AM.
It's actually located in the T2 car park (parking garage) and the signage isn't great. It's on the arrival level of T2.
I've stayed many times and I will be back in two weeks.
However, It will cost more than $130 which is about 97 GBP.
There is also a Hilton Garden Inn near the Hatton Cross tube station. It's one station before Heathrow. Their rates are usually lower.
Don't get the two hotels confused.
Two things to take into consideration for the latter: If this is a weekend, make sure there are no planned engineering works that would shut the Piccadilly line near Heathrow. If you do decide to stay there and take the tube in, get one for T5 and not T4. Why? The one for T5 goes from Hatton Cross to Heathrow T2 & 3. The one for T4 first stops at T4 and sits there for nine minutes so the driver can get a break. It then goes on to T2 & 3.