I respectfully disagree. Bodden Town is a nice area, b-i-l's family stayed at TNI also but for every single dive he drove to Ocean Frontiers on the East End (south side) or back to Georgetown - 15-20mins. each way There's little (no?) food shopping there and most dining options are back to Georgetown. Ocean Frontiers is all boat diving only - there really isn't any good shore diving on the East End - although it's the most pristine diving left on GC.
A month's worth of boat diving, even at some negotiated rate is going to be extremely expensive when you consider the standard rate is 2 dives for $100ish. Most operators do offer some discount for multiple days - Ambassador for ex. offers 4 2-tank dives for $360 but since it's possible to do 4 dives/day...
What I'd look at instead is locating in a non-touristy (if such a thing exists) neighborhood near dive sites/operators. Probably not near Georgetown either - the 4-5 daily cruise ship arrivals make that a mess till about 4PM every day.
I'd look for something basically north of the Ritz in West Bay/NW Point. It's quieter, the cruise traffic doesn't generally get that far (exceptions being the tour buses to the Sandbar Snorkel, Boatswains Beach/Turtle Farm and Tortuga Rum cake factory.
NW Point also has the advantage of being under 10mins. drive from all the activities/nightlife/restaurants on Seven Mile Beach. Many of the boat based operators work out of one of several marinas near there - if you did rent a condo on SMB, they would pick you up. Farther north you might have to drive over. There's also a Foster's Food Fair in West Bay.
A further advantage is that arguably the three best shore dives are in that area - Turtle Reef, Lighthouse Point and Cobalt Coast. Sundivers is on-site at TR for tank rentals and the others both have a Divetech shop on premises. There's also Coconut Bay and Bonnie's Arch condos in the same area - both are on "private" shore dives since they have a ladder down from the ironshore cliffs for their guests use only. A couple of the units at Coconut are owned by the owner of Stingray Watesports and he offered to hook us up with tanks for shore diving as well. Check on vrbo.com - there's several units often for rent on either property.
You'll also see a lot of rentals on the NE side of the island - Rum Point, Old Man Bay etc. Understand that for a newer diver, that's all boat diving with Tortuga Divers at Morritt's (a big condo/timeshare complex) or Silver Sands at the Reef Resort. There is no shore diving to speak of in that area that doesn't require a surface swim thru an active boat channel. There's also one small food market, maybe 1/2 dozen restaurants counting ones at the resorts and Georgetown is 45mins+ drive from there. Some people really like the peace/quiet staying in that area affords - not for me personally.
The other cluster of shore dives is in town. Eden Rock/Devils Grotto, Foster's Reef, Sunset House, Smith's Cove etc. The first two are a short distance from the cruise port - there can be as many as 4-5 ships in port daily - so that changes the entire town till about 4pm. After that it's nice. Eden Rock is also one of few places that rent tanks for off-site use - the other being Divers Supply in West Bay. All the on-site operators at the other sites provide tanks/weights for use on premises only.
You won't need weights either. Although you'll likely find that it's cheaper to buy weights on arrival and leave them when you go since there is a charge at some operators. Or bring them with you - over the long term that would certainly be cheaper.
It might even be cheaper to do that with a tank - you should price that both ways. I'd guess just about any operator would fill it as needed. I might even consider buying a tank here, pulling the valve (for TSA) and bringing it. You'd pay once for a VIP before the 1st operator would fill it, after that it's yours for the month for the cost/time of a fill. Offer it to someone locally and get some money back when you leave.