Tien Giang province is the closest Mekong Delta province to Saigon and is a very popular destination for organised tours out of Saigon. The same-named provincial capital sits on the northern bank of the Mekong (Tien Giang) River and has a number of offshore islands that can be visited.
Unfortunately the local authorities have taken a somewhat uninspired view of tourism development here, meaning that unless you are willing to joing a larger tour, travelling around this part of the river independently is prohibitively expensive.
Most tours throughout Tien Giang province run in boats that seat 20-plus people and while such numbers bring costs down to a more reasonable level, the downside is you'll visit attractions en masse and be herded around. If you're interested in exploring riverine life, we'd suggest heading across the river to Ben Tre or further south to Can Tho or west to Chau Doc, where prices far more reasonable and well-tailored to independent travellers.
My Tho town, a medium-sized Mekong Delta provincial capital, has a bit of an abandoned feel to it, except during the morning when busloads of tourists from Saigon descend to do a boat trip to the nearby islands.
Aside from the morning, you can often have the riverbank entirely to yourself -- local tourist authorities are yet to commence charging foreigners to enjoy the view, so you can at least plan for doing that.
Aside from doing an overpriced boat-trip, one reason to visit My Tho is to catch a cargo boat west to Chau Doc. This 17-hour trip is a priceless way to see river life, as long as you do not mind roughing it a little. The boats do not leave every day, but you can ask either at the cargo pier (western edge of town), or keep an eye out for Mr Nip (he'll most likely find you), a cyclo driver who speaks excellent English and is a fountain of knowledge about My Tho.