I think you're looking at this from the wrong perspective.
I bought a Manfrotto Compact Photo Tripod MKC3-PF - White for £50 and also its dedicated Manfrotto case. Upshot is i have a tripod in a case that is no bigger than my wife's fore arm, and she is only 5ft 3".
I also purchased a Manfrotto Stile Bella IV Shoulder Bag Cord, which adequately holds all you are asking of it, with room for mobile phone and wallet.
I can assure you, neither bag/ case is large to carry, or heavy. And with it being in 2 parts, i'm not afraid to leave the tripod section in the hotel room. So small is it, that it will fit in the suitcase whilst you are out exploring.
All 3 items came to no more than £100 (tripod, case & camera bag) and are all of great quality whilst being light. Much better than lugging every thing else around.
It really doesn't get any smaller or lighter than that, and much more conspicuous than a medium to large Lowepro bag or similar.